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prev_sample = prev_sample + variance if not return_dict: return ( prev_sample, pred_original_sample, ) return DDIMParallelSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample) def batch_step_no_noise( self, model_output: torch.Tensor, timesteps: List[int], sample: torch.Tensor, eta: float = 0.0, use_clipped_model_output: bool = False, ) -> torch.Tensor: """ Batched version of the `step` function, to be able to reverse the SDE for multiple samples/timesteps at once. Also, does not add any noise to the predicted sample, which is necessary for parallel sampling where the noise is pre-sampled by the pipeline. Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise).
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Args: model_output (`torch.Tensor`): direct output from learned diffusion model. timesteps (`List[int]`): current discrete timesteps in the diffusion chain. This is now a list of integers. sample (`torch.Tensor`): current instance of sample being created by diffusion process. eta (`float`): weight of noise for added noise in diffusion step. use_clipped_model_output (`bool`): if `True`, compute "corrected" `model_output` from the clipped predicted original sample. Necessary because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no clipping has happened, "corrected" `model_output` would coincide with the one provided as input and `use_clipped_model_output` will have not effect. Returns: `torch.Tensor`: sample tensor at previous timestep.
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""" if self.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) assert eta == 0.0 # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf # Ideally, read DDIM paper in-detail understanding # Notation (<variable name> -> <name in paper> # - pred_noise_t -> e_theta(x_t, t) # - pred_original_sample -> f_theta(x_t, t) or x_0 # - std_dev_t -> sigma_t # - eta -> η # - pred_sample_direction -> "direction pointing to x_t" # - pred_prev_sample -> "x_t-1" # 1. get previous step value (=t-1) t = timesteps prev_t = t - self.config.num_train_timesteps // self.num_inference_steps t = t.view(-1, *([1] * (model_output.ndim - 1))) prev_t = prev_t.view(-1, *([1] * (model_output.ndim - 1)))
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# 1. compute alphas, betas self.alphas_cumprod = self.alphas_cumprod.to(model_output.device) self.final_alpha_cumprod = self.final_alpha_cumprod.to(model_output.device) alpha_prod_t = self.alphas_cumprod[t] alpha_prod_t_prev = self.alphas_cumprod[torch.clip(prev_t, min=0)] alpha_prod_t_prev[prev_t < 0] = torch.tensor(1.0) beta_prod_t = 1 - alpha_prod_t
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# 3. compute predicted original sample from predicted noise also called # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf if self.config.prediction_type == "epsilon": pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5) pred_epsilon = model_output elif self.config.prediction_type == "sample": pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) elif self.config.prediction_type == "v_prediction": pred_original_sample = (alpha_prod_t**0.5) * sample - (beta_prod_t**0.5) * model_output pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`"
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)
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# 4. Clip or threshold "predicted x_0" if self.config.thresholding: pred_original_sample = self._threshold_sample(pred_original_sample) elif self.config.clip_sample: pred_original_sample = pred_original_sample.clamp( -self.config.clip_sample_range, self.config.clip_sample_range ) # 5. compute variance: "sigma_t(η)" -> see formula (16) # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1) variance = self._batch_get_variance(t, prev_t).to(model_output.device).view(*alpha_prod_t_prev.shape) std_dev_t = eta * variance ** (0.5) if use_clipped_model_output: # the pred_epsilon is always re-derived from the clipped x_0 in Glide pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
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# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * pred_epsilon # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction return prev_sample
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# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor, ) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as original_samples # Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement # for the subsequent add_noise calls self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device) alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype) timesteps = timesteps.to(original_samples.device) sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(original_samples.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)
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sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise return noisy_samples # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor: # Make sure alphas_cumprod and timestep have same device and dtype as sample self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device) alphas_cumprod = self.alphas_cumprod.to(dtype=sample.dtype) timesteps = timesteps.to(sample.device)
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sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5 sqrt_alpha_prod = sqrt_alpha_prod.flatten() while len(sqrt_alpha_prod.shape) < len(sample.shape): sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1) sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5 sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten() while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape): sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1) velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample return velocity def __len__(self): return self.config.num_train_timesteps
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class DDPMWuerstchenSchedulerOutput(BaseOutput): """ Output class for the scheduler's step function output. Args: prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the denoising loop. """ prev_sample: torch.Tensor
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class DDPMWuerstchenScheduler(SchedulerMixin, ConfigMixin): """ Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and Langevin dynamics sampling. [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__` function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`. [`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and [`~SchedulerMixin.from_pretrained`] functions. For more details, see the original paper: https://arxiv.org/abs/2006.11239 Args: scaler (`float`): .... s (`float`): .... """
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@register_to_config def __init__( self, scaler: float = 1.0, s: float = 0.008, ): self.scaler = scaler self.s = torch.tensor([s]) self._init_alpha_cumprod = torch.cos(self.s / (1 + self.s) * torch.pi * 0.5) ** 2 # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 def _alpha_cumprod(self, t, device): if self.scaler > 1: t = 1 - (1 - t) ** self.scaler elif self.scaler < 1: t = t**self.scaler alpha_cumprod = torch.cos( (t + self.s.to(device)) / (1 + self.s.to(device)) * torch.pi * 0.5 ) ** 2 / self._init_alpha_cumprod.to(device) return alpha_cumprod.clamp(0.0001, 0.9999) def scale_model_input(self, sample: torch.Tensor, timestep: Optional[int] = None) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep.
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Args: sample (`torch.Tensor`): input sample timestep (`int`, optional): current timestep Returns: `torch.Tensor`: scaled input sample """ return sample def set_timesteps( self, num_inference_steps: int = None, timesteps: Optional[List[int]] = None, device: Union[str, torch.device] = None, ): """ Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
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Args: num_inference_steps (`Dict[float, int]`): the number of diffusion steps used when generating samples with a pre-trained model. If passed, then `timesteps` must be `None`. device (`str` or `torch.device`, optional): the device to which the timesteps are moved to. {2 / 3: 20, 0.0: 10} """ if timesteps is None: timesteps = torch.linspace(1.0, 0.0, num_inference_steps + 1, device=device) if not isinstance(timesteps, torch.Tensor): timesteps = torch.Tensor(timesteps).to(device) self.timesteps = timesteps
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def step( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, generator=None, return_dict: bool = True, ) -> Union[DDPMWuerstchenSchedulerOutput, Tuple]: """ Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise). Args: model_output (`torch.Tensor`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`torch.Tensor`): current instance of sample being created by diffusion process. generator: random number generator. return_dict (`bool`): option for returning tuple rather than DDPMWuerstchenSchedulerOutput class
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Returns: [`DDPMWuerstchenSchedulerOutput`] or `tuple`: [`DDPMWuerstchenSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ dtype = model_output.dtype device = model_output.device t = timestep prev_t = self.previous_timestep(t) alpha_cumprod = self._alpha_cumprod(t, device).view(t.size(0), *[1 for _ in sample.shape[1:]]) alpha_cumprod_prev = self._alpha_cumprod(prev_t, device).view(prev_t.size(0), *[1 for _ in sample.shape[1:]]) alpha = alpha_cumprod / alpha_cumprod_prev mu = (1.0 / alpha).sqrt() * (sample - (1 - alpha) * model_output / (1 - alpha_cumprod).sqrt())
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std_noise = randn_tensor(mu.shape, generator=generator, device=model_output.device, dtype=model_output.dtype) std = ((1 - alpha) * (1.0 - alpha_cumprod_prev) / (1.0 - alpha_cumprod)).sqrt() * std_noise pred = mu + std * (prev_t != 0).float().view(prev_t.size(0), *[1 for _ in sample.shape[1:]]) if not return_dict: return (pred.to(dtype),) return DDPMWuerstchenSchedulerOutput(prev_sample=pred.to(dtype)) def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.Tensor, ) -> torch.Tensor: device = original_samples.device dtype = original_samples.dtype alpha_cumprod = self._alpha_cumprod(timesteps, device=device).view( timesteps.size(0), *[1 for _ in original_samples.shape[1:]] ) noisy_samples = alpha_cumprod.sqrt() * original_samples + (1 - alpha_cumprod).sqrt() * noise return noisy_samples.to(dtype=dtype)
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def __len__(self): return self.config.num_train_timesteps def previous_timestep(self, timestep): index = (self.timesteps - timestep[0]).abs().argmin().item() prev_t = self.timesteps[index + 1][None].expand(timestep.shape[0]) return prev_t
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class FlaxKarrasDiffusionSchedulers(Enum): FlaxDDIMScheduler = 1 FlaxDDPMScheduler = 2 FlaxPNDMScheduler = 3 FlaxLMSDiscreteScheduler = 4 FlaxDPMSolverMultistepScheduler = 5 FlaxEulerDiscreteScheduler = 6
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class FlaxSchedulerOutput(BaseOutput): """ Base class for the scheduler's step function output. Args: prev_sample (`jnp.ndarray` of shape `(batch_size, num_channels, height, width)` for images): Computed sample (x_{t-1}) of previous timestep. `prev_sample` should be used as next model input in the denoising loop. """ prev_sample: jnp.ndarray
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class FlaxSchedulerMixin(PushToHubMixin): """ Mixin containing common functions for the schedulers. Class attributes: - **_compatibles** (`List[str]`) -- A list of classes that are compatible with the parent class, so that `from_config` can be used from a class different than the one used to save the config (should be overridden by parent class). """ config_name = SCHEDULER_CONFIG_NAME ignore_for_config = ["dtype"] _compatibles = [] has_compatibles = True @classmethod @validate_hf_hub_args def from_pretrained( cls, pretrained_model_name_or_path: Optional[Union[str, os.PathLike]] = None, subfolder: Optional[str] = None, return_unused_kwargs=False, **kwargs, ): r""" Instantiate a Scheduler class from a pre-defined JSON-file. Parameters: pretrained_model_name_or_path (`str` or `os.PathLike`, *optional*): Can be either:
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- A string, the *model id* of a model repo on huggingface.co. Valid model ids should have an organization name, like `google/ddpm-celebahq-256`. - A path to a *directory* containing model weights saved using [`~SchedulerMixin.save_pretrained`], e.g., `./my_model_directory/`. subfolder (`str`, *optional*): In case the relevant files are located inside a subfolder of the model repo (either remote in huggingface.co or downloaded locally), you can specify the folder name here. return_unused_kwargs (`bool`, *optional*, defaults to `False`): Whether kwargs that are not consumed by the Python class should be returned or not.
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cache_dir (`Union[str, os.PathLike]`, *optional*): Path to a directory in which a downloaded pretrained model configuration should be cached if the standard cache should not be used. force_download (`bool`, *optional*, defaults to `False`): Whether or not to force the (re-)download of the model weights and configuration files, overriding the cached versions if they exist.
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proxies (`Dict[str, str]`, *optional*): A dictionary of proxy servers to use by protocol or endpoint, e.g., `{'http': 'foo.bar:3128', 'http://hostname': 'foo.bar:4012'}`. The proxies are used on each request. output_loading_info(`bool`, *optional*, defaults to `False`): Whether or not to also return a dictionary containing missing keys, unexpected keys and error messages. local_files_only(`bool`, *optional*, defaults to `False`): Whether or not to only look at local files (i.e., do not try to download the model). token (`str` or *bool*, *optional*): The token to use as HTTP bearer authorization for remote files. If `True`, will use the token generated when running `transformers-cli login` (stored in `~/.huggingface`). revision (`str`, *optional*, defaults to `"main"`):
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The specific model version to use. It can be a branch name, a tag name, or a commit id, since we use a git-based system for storing models and other artifacts on huggingface.co, so `revision` can be any identifier allowed by git.
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<Tip> It is required to be logged in (`huggingface-cli login`) when you want to use private or [gated models](https://huggingface.co./docs/hub/models-gated#gated-models). </Tip> <Tip> Activate the special ["offline-mode"](https://huggingface.co./transformers/installation.html#offline-mode) to use this method in a firewalled environment. </Tip> """ config, kwargs = cls.load_config( pretrained_model_name_or_path=pretrained_model_name_or_path, subfolder=subfolder, return_unused_kwargs=True, **kwargs, ) scheduler, unused_kwargs = cls.from_config(config, return_unused_kwargs=True, **kwargs) if hasattr(scheduler, "create_state") and getattr(scheduler, "has_state", False): state = scheduler.create_state() if return_unused_kwargs: return scheduler, state, unused_kwargs return scheduler, state
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def save_pretrained(self, save_directory: Union[str, os.PathLike], push_to_hub: bool = False, **kwargs): """ Save a scheduler configuration object to the directory `save_directory`, so that it can be re-loaded using the [`~FlaxSchedulerMixin.from_pretrained`] class method.
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Args: save_directory (`str` or `os.PathLike`): Directory where the configuration JSON file will be saved (will be created if it does not exist). push_to_hub (`bool`, *optional*, defaults to `False`): Whether or not to push your model to the Hugging Face Hub after saving it. You can specify the repository you want to push to with `repo_id` (will default to the name of `save_directory` in your namespace). kwargs (`Dict[str, Any]`, *optional*): Additional keyword arguments passed along to the [`~utils.PushToHubMixin.push_to_hub`] method. """ self.save_config(save_directory=save_directory, push_to_hub=push_to_hub, **kwargs) @property def compatibles(self): """ Returns all schedulers that are compatible with this scheduler
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Returns: `List[SchedulerMixin]`: List of compatible schedulers """ return self._get_compatibles() @classmethod def _get_compatibles(cls): compatible_classes_str = list(set([cls.__name__] + cls._compatibles)) diffusers_library = importlib.import_module(__name__.split(".")[0]) compatible_classes = [ getattr(diffusers_library, c) for c in compatible_classes_str if hasattr(diffusers_library, c) ] return compatible_classes
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class CommonSchedulerState: alphas: jnp.ndarray betas: jnp.ndarray alphas_cumprod: jnp.ndarray @classmethod def create(cls, scheduler): config = scheduler.config
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if config.trained_betas is not None: betas = jnp.asarray(config.trained_betas, dtype=scheduler.dtype) elif config.beta_schedule == "linear": betas = jnp.linspace(config.beta_start, config.beta_end, config.num_train_timesteps, dtype=scheduler.dtype) elif config.beta_schedule == "scaled_linear": # this schedule is very specific to the latent diffusion model. betas = ( jnp.linspace( config.beta_start**0.5, config.beta_end**0.5, config.num_train_timesteps, dtype=scheduler.dtype ) ** 2 ) elif config.beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule betas = betas_for_alpha_bar(config.num_train_timesteps, dtype=scheduler.dtype) else: raise NotImplementedError( f"beta_schedule {config.beta_schedule} is not implemented for scheduler {scheduler.__class__.__name__}" )
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alphas = 1.0 - betas alphas_cumprod = jnp.cumprod(alphas, axis=0) return cls( alphas=alphas, betas=betas, alphas_cumprod=alphas_cumprod, )
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class SdeVeOutput(BaseOutput): """ Output class for the scheduler's `step` function output. Args: prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the denoising loop. prev_sample_mean (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): Mean averaged `prev_sample` over previous timesteps. """ prev_sample: torch.Tensor prev_sample_mean: torch.Tensor
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class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin): """ `ScoreSdeVeScheduler` is a variance exploding stochastic differential equation (SDE) scheduler. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.
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Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. snr (`float`, defaults to 0.15): A coefficient weighting the step from the `model_output` sample (from the network) to the random noise. sigma_min (`float`, defaults to 0.01): The initial noise scale for the sigma sequence in the sampling procedure. The minimum sigma should mirror the distribution of the data. sigma_max (`float`, defaults to 1348.0): The maximum value used for the range of continuous timesteps passed into the model. sampling_eps (`float`, defaults to 1e-5): The end value of sampling where timesteps decrease progressively from 1 to epsilon. correct_steps (`int`, defaults to 1): The number of correction steps performed on a produced sample. """ order = 1
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@register_to_config def __init__( self, num_train_timesteps: int = 2000, snr: float = 0.15, sigma_min: float = 0.01, sigma_max: float = 1348.0, sampling_eps: float = 1e-5, correct_steps: int = 1, ): # standard deviation of the initial noise distribution self.init_noise_sigma = sigma_max # setable values self.timesteps = None self.set_sigmas(num_train_timesteps, sigma_min, sigma_max, sampling_eps) def scale_model_input(self, sample: torch.Tensor, timestep: Optional[int] = None) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: sample (`torch.Tensor`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain.
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Returns: `torch.Tensor`: A scaled input sample. """ return sample def set_timesteps( self, num_inference_steps: int, sampling_eps: float = None, device: Union[str, torch.device] = None ): """ Sets the continuous timesteps used for the diffusion chain (to be run before inference). Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. sampling_eps (`float`, *optional*): The final timestep value (overrides value given during scheduler instantiation). device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. """ sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps
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self.timesteps = torch.linspace(1, sampling_eps, num_inference_steps, device=device) def set_sigmas( self, num_inference_steps: int, sigma_min: float = None, sigma_max: float = None, sampling_eps: float = None ): """ Sets the noise scales used for the diffusion chain (to be run before inference). The sigmas control the weight of the `drift` and `diffusion` components of the sample update.
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. sigma_min (`float`, optional): The initial noise scale value (overrides value given during scheduler instantiation). sigma_max (`float`, optional): The final noise scale value (overrides value given during scheduler instantiation). sampling_eps (`float`, optional): The final timestep value (overrides value given during scheduler instantiation). """ sigma_min = sigma_min if sigma_min is not None else self.config.sigma_min sigma_max = sigma_max if sigma_max is not None else self.config.sigma_max sampling_eps = sampling_eps if sampling_eps is not None else self.config.sampling_eps if self.timesteps is None: self.set_timesteps(num_inference_steps, sampling_eps)
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self.sigmas = sigma_min * (sigma_max / sigma_min) ** (self.timesteps / sampling_eps) self.discrete_sigmas = torch.exp(torch.linspace(math.log(sigma_min), math.log(sigma_max), num_inference_steps)) self.sigmas = torch.tensor([sigma_min * (sigma_max / sigma_min) ** t for t in self.timesteps]) def get_adjacent_sigma(self, timesteps, t): return torch.where( timesteps == 0, torch.zeros_like(t.to(timesteps.device)), self.discrete_sigmas[timesteps - 1].to(timesteps.device), ) def step_pred( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, generator: Optional[torch.Generator] = None, return_dict: bool = True, ) -> Union[SdeVeOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion process from the learned model outputs (most often the predicted noise).
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`. Returns: [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_sde_ve.SdeVeOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor.
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""" if self.timesteps is None: raise ValueError( "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler" ) timestep = timestep * torch.ones( sample.shape[0], device=sample.device ) # torch.repeat_interleave(timestep, sample.shape[0]) timesteps = (timestep * (len(self.timesteps) - 1)).long() # mps requires indices to be in the same device, so we use cpu as is the default with cuda timesteps = timesteps.to(self.discrete_sigmas.device) sigma = self.discrete_sigmas[timesteps].to(sample.device) adjacent_sigma = self.get_adjacent_sigma(timesteps, timestep).to(sample.device) drift = torch.zeros_like(sample) diffusion = (sigma**2 - adjacent_sigma**2) ** 0.5
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# equation 6 in the paper: the model_output modeled by the network is grad_x log pt(x) # also equation 47 shows the analog from SDE models to ancestral sampling methods diffusion = diffusion.flatten() while len(diffusion.shape) < len(sample.shape): diffusion = diffusion.unsqueeze(-1) drift = drift - diffusion**2 * model_output # equation 6: sample noise for the diffusion term of noise = randn_tensor( sample.shape, layout=sample.layout, generator=generator, device=sample.device, dtype=sample.dtype ) prev_sample_mean = sample - drift # subtract because `dt` is a small negative timestep # TODO is the variable diffusion the correct scaling term for the noise? prev_sample = prev_sample_mean + diffusion * noise # add impact of diffusion field g if not return_dict: return (prev_sample, prev_sample_mean)
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return SdeVeOutput(prev_sample=prev_sample, prev_sample_mean=prev_sample_mean) def step_correct( self, model_output: torch.Tensor, sample: torch.Tensor, generator: Optional[torch.Generator] = None, return_dict: bool = True, ) -> Union[SchedulerOutput, Tuple]: """ Correct the predicted sample based on the `model_output` of the network. This is often run repeatedly after making the prediction for the previous timestep. Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`.
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Returns: [`~schedulers.scheduling_sde_ve.SdeVeOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_sde_ve.SdeVeOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.timesteps is None: raise ValueError( "`self.timesteps` is not set, you need to run 'set_timesteps' after creating the scheduler" ) # For small batch sizes, the paper "suggest replacing norm(z) with sqrt(d), where d is the dim. of z" # sample noise for correction noise = randn_tensor(sample.shape, layout=sample.layout, generator=generator).to(sample.device)
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# compute step size from the model_output, the noise, and the snr grad_norm = torch.norm(model_output.reshape(model_output.shape[0], -1), dim=-1).mean() noise_norm = torch.norm(noise.reshape(noise.shape[0], -1), dim=-1).mean() step_size = (self.config.snr * noise_norm / grad_norm) ** 2 * 2 step_size = step_size * torch.ones(sample.shape[0]).to(sample.device) # self.repeat_scalar(step_size, sample.shape[0]) # compute corrected sample: model_output term and noise term step_size = step_size.flatten() while len(step_size.shape) < len(sample.shape): step_size = step_size.unsqueeze(-1) prev_sample_mean = sample + step_size * model_output prev_sample = prev_sample_mean + ((step_size * 2) ** 0.5) * noise if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample)
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def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.Tensor, ) -> torch.Tensor: # Make sure sigmas and timesteps have the same device and dtype as original_samples timesteps = timesteps.to(original_samples.device) sigmas = self.discrete_sigmas.to(original_samples.device)[timesteps] noise = ( noise * sigmas[:, None, None, None] if noise is not None else torch.randn_like(original_samples) * sigmas[:, None, None, None] ) noisy_samples = noise + original_samples return noisy_samples def __len__(self): return self.config.num_train_timesteps
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class IPNDMScheduler(SchedulerMixin, ConfigMixin): """ A fourth-order Improved Pseudo Linear Multistep scheduler. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving. Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. """ order = 1 @register_to_config def __init__( self, num_train_timesteps: int = 1000, trained_betas: Optional[Union[np.ndarray, List[float]]] = None ): # set `betas`, `alphas`, `timesteps` self.set_timesteps(num_train_timesteps) # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0
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# For now we only support F-PNDM, i.e. the runge-kutta method # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf # mainly at formula (9), (12), (13) and the Algorithm 2. self.pndm_order = 4 # running values self.ets = [] self._step_index = None self._begin_index = None @property def step_index(self): """ The index counter for current timestep. It will increase 1 after each scheduler step. """ return self._step_index @property def begin_index(self): """ The index for the first timestep. It should be set from pipeline with `set_begin_index` method. """ return self._begin_index
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index def set_begin_index(self, begin_index: int = 0): """ Sets the begin index for the scheduler. This function should be run from pipeline before the inference. Args: begin_index (`int`): The begin index for the scheduler. """ self._begin_index = begin_index def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. """ self.num_inference_steps = num_inference_steps steps = torch.linspace(1, 0, num_inference_steps + 1)[:-1] steps = torch.cat([steps, torch.tensor([0.0])]) if self.config.trained_betas is not None: self.betas = torch.tensor(self.config.trained_betas, dtype=torch.float32) else: self.betas = torch.sin(steps * math.pi / 2) ** 2 self.alphas = (1.0 - self.betas**2) ** 0.5 timesteps = (torch.atan2(self.betas, self.alphas) / math.pi * 2)[:-1] self.timesteps = timesteps.to(device) self.ets = [] self._step_index = None self._begin_index = None
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.index_for_timestep def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps indices = (schedule_timesteps == timestep).nonzero() # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) pos = 1 if len(indices) > 1 else 0 return indices[pos].item()
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._init_step_index def _init_step_index(self, timestep): if self.begin_index is None: if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) self._step_index = self.index_for_timestep(timestep) else: self._step_index = self._begin_index def step( self, model_output: torch.Tensor, timestep: Union[int, torch.Tensor], sample: torch.Tensor, return_dict: bool = True, ) -> Union[SchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the linear multistep method. It performs one forward pass multiple times to approximate the solution.
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. return_dict (`bool`): Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or tuple.
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Returns: [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) if self.step_index is None: self._init_step_index(timestep) timestep_index = self.step_index prev_timestep_index = self.step_index + 1 ets = sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index] self.ets.append(ets)
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if len(self.ets) == 1: ets = self.ets[-1] elif len(self.ets) == 2: ets = (3 * self.ets[-1] - self.ets[-2]) / 2 elif len(self.ets) == 3: ets = (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12 else: ets = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4]) prev_sample = self._get_prev_sample(sample, timestep_index, prev_timestep_index, ets) # upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: sample (`torch.Tensor`): The input sample.
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Returns: `torch.Tensor`: A scaled input sample. """ return sample def _get_prev_sample(self, sample, timestep_index, prev_timestep_index, ets): alpha = self.alphas[timestep_index] sigma = self.betas[timestep_index] next_alpha = self.alphas[prev_timestep_index] next_sigma = self.betas[prev_timestep_index] pred = (sample - sigma * ets) / max(alpha, 1e-8) prev_sample = next_alpha * pred + ets * next_sigma return prev_sample def __len__(self): return self.config.num_train_timesteps
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class DEISMultistepScheduler(SchedulerMixin, ConfigMixin): """ `DEISMultistepScheduler` is a fast high order solver for diffusion ordinary differential equations (ODEs). This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving.
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Args: num_train_timesteps (`int`, defaults to 1000): The number of diffusion steps to train the model. beta_start (`float`, defaults to 0.0001): The starting `beta` value of inference. beta_end (`float`, defaults to 0.02): The final `beta` value. beta_schedule (`str`, defaults to `"linear"`): The beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from `linear`, `scaled_linear`, or `squaredcos_cap_v2`. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. solver_order (`int`, defaults to 2): The DEIS order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided sampling, and `solver_order=3` for unconditional sampling. prediction_type (`str`, defaults to `epsilon`):
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Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process), `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen Video](https://imagen.research.google/video/paper.pdf) paper). thresholding (`bool`, defaults to `False`): Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such as Stable Diffusion. dynamic_thresholding_ratio (`float`, defaults to 0.995): The ratio for the dynamic thresholding method. Valid only when `thresholding=True`. sample_max_value (`float`, defaults to 1.0): The threshold value for dynamic thresholding. Valid only when `thresholding=True`. algorithm_type (`str`, defaults to `deis`): The algorithm type for the solver. lower_order_final (`bool`, defaults to `True`):
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Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps. use_karras_sigmas (`bool`, *optional*, defaults to `False`): Whether to use Karras sigmas for step sizes in the noise schedule during the sampling process. If `True`, the sigmas are determined according to a sequence of noise levels {σi}. use_exponential_sigmas (`bool`, *optional*, defaults to `False`): Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process. use_beta_sigmas (`bool`, *optional*, defaults to `False`): Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta Sampling is All You Need](https://huggingface.co./papers/2407.12173) for more information. timestep_spacing (`str`, defaults to `"linspace"`):
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The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and Sample Steps are Flawed](https://huggingface.co./papers/2305.08891) for more information. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. """
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_compatibles = [e.name for e in KarrasDiffusionSchedulers] order = 1
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@register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.0001, beta_end: float = 0.02, beta_schedule: str = "linear", trained_betas: Optional[np.ndarray] = None, solver_order: int = 2, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, algorithm_type: str = "deis", solver_type: str = "logrho", lower_order_final: bool = True, use_karras_sigmas: Optional[bool] = False, use_exponential_sigmas: Optional[bool] = False, use_beta_sigmas: Optional[bool] = False, use_flow_sigmas: Optional[bool] = False, flow_shift: Optional[float] = 1.0, timestep_spacing: str = "linspace", steps_offset: int = 0, ): if self.config.use_beta_sigmas and not is_scipy_available():
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raise ImportError("Make sure to install scipy if you want to use beta sigmas.") if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1: raise ValueError( "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used." ) if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear": self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) elif beta_schedule == "scaled_linear": # this schedule is very specific to the latent diffusion model. self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2 elif beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule
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self.betas = betas_for_alpha_bar(num_train_timesteps) else: raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")
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self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # Currently we only support VP-type noise schedule self.alpha_t = torch.sqrt(self.alphas_cumprod) self.sigma_t = torch.sqrt(1 - self.alphas_cumprod) self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t) self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5 # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 # settings for DEIS if algorithm_type not in ["deis"]: if algorithm_type in ["dpmsolver", "dpmsolver++"]: self.register_to_config(algorithm_type="deis") else: raise NotImplementedError(f"{algorithm_type} is not implemented for {self.__class__}")
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if solver_type not in ["logrho"]: if solver_type in ["midpoint", "heun", "bh1", "bh2"]: self.register_to_config(solver_type="logrho") else: raise NotImplementedError(f"solver type {solver_type} is not implemented for {self.__class__}") # setable values self.num_inference_steps = None timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=np.float32)[::-1].copy() self.timesteps = torch.from_numpy(timesteps) self.model_outputs = [None] * solver_order self.lower_order_nums = 0 self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication @property def step_index(self): """ The index counter for current timestep. It will increase 1 after each scheduler step. """ return self._step_index
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@property def begin_index(self): """ The index for the first timestep. It should be set from pipeline with `set_begin_index` method. """ return self._begin_index # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index def set_begin_index(self, begin_index: int = 0): """ Sets the begin index for the scheduler. This function should be run from pipeline before the inference. Args: begin_index (`int`): The begin index for the scheduler. """ self._begin_index = begin_index def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. """ # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891 if self.config.timestep_spacing == "linspace": timesteps = ( np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps + 1) .round()[::-1][:-1] .copy() .astype(np.int64) ) elif self.config.timestep_spacing == "leading": step_ratio = self.config.num_train_timesteps // (num_inference_steps + 1) # creates integer timesteps by multiplying by ratio
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# casting to int to avoid issues when num_inference_step is power of 3 timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[::-1][:-1].copy().astype(np.int64) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / num_inference_steps # creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = np.arange(self.config.num_train_timesteps, 0, -step_ratio).round().copy().astype(np.int64) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'." )
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sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) log_sigmas = np.log(sigmas) if self.config.use_karras_sigmas: sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round() sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32) elif self.config.use_exponential_sigmas: sigmas = np.flip(sigmas).copy() sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32) elif self.config.use_beta_sigmas: sigmas = np.flip(sigmas).copy()
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sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=num_inference_steps) timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]) sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32) elif self.config.use_flow_sigmas: alphas = np.linspace(1, 1 / self.config.num_train_timesteps, num_inference_steps + 1) sigmas = 1.0 - alphas sigmas = np.flip(self.config.flow_shift * sigmas / (1 + (self.config.flow_shift - 1) * sigmas))[:-1].copy() timesteps = (sigmas * self.config.num_train_timesteps).copy() sigmas = np.concatenate([sigmas, sigmas[-1:]]).astype(np.float32) else: sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas) sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5 sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
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self.sigmas = torch.from_numpy(sigmas) self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64) self.num_inference_steps = len(timesteps) self.model_outputs = [ None, ] * self.config.solver_order self.lower_order_nums = 0 # add an index counter for schedulers that allow duplicated timesteps self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication
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# Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor: """ "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing pixels from saturation at each step. We find that dynamic thresholding results in significantly better photorealism as well as better image-text alignment, especially when using very large guidance weights." https://arxiv.org/abs/2205.11487 """ dtype = sample.dtype batch_size, channels, *remaining_dims = sample.shape
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if dtype not in (torch.float32, torch.float64): sample = sample.float() # upcast for quantile calculation, and clamp not implemented for cpu half # Flatten sample for doing quantile calculation along each image sample = sample.reshape(batch_size, channels * np.prod(remaining_dims)) abs_sample = sample.abs() # "a certain percentile absolute pixel value" s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1) s = torch.clamp( s, min=1, max=self.config.sample_max_value ) # When clamped to min=1, equivalent to standard clipping to [-1, 1] s = s.unsqueeze(1) # (batch_size, 1) because clamp will broadcast along dim=0 sample = torch.clamp(sample, -s, s) / s # "we threshold xt0 to the range [-s, s] and then divide by s" sample = sample.reshape(batch_size, channels, *remaining_dims) sample = sample.to(dtype) return sample
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t def _sigma_to_t(self, sigma, log_sigmas): # get log sigma log_sigma = np.log(np.maximum(sigma, 1e-10)) # get distribution dists = log_sigma - log_sigmas[:, np.newaxis] # get sigmas range low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2) high_idx = low_idx + 1 low = log_sigmas[low_idx] high = log_sigmas[high_idx] # interpolate sigmas w = (low - log_sigma) / (low - high) w = np.clip(w, 0, 1) # transform interpolation to time range t = (1 - w) * low_idx + w * high_idx t = t.reshape(sigma.shape) return t
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# Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t def _sigma_to_alpha_sigma_t(self, sigma): if self.config.use_flow_sigmas: alpha_t = 1 - sigma sigma_t = sigma else: alpha_t = 1 / ((sigma**2 + 1) ** 0.5) sigma_t = sigma * alpha_t return alpha_t, sigma_t # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor: """Constructs the noise schedule of Karras et al. (2022).""" # Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None
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if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item() rho = 7.0 # 7.0 is the value used in the paper ramp = np.linspace(0, 1, num_inference_steps) min_inv_rho = sigma_min ** (1 / rho) max_inv_rho = sigma_max ** (1 / rho) sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho return sigmas # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_exponential def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor: """Constructs an exponential noise schedule."""
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# Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item() sigmas = np.exp(np.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps)) return sigmas
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# Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta def _convert_to_beta( self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6 ) -> torch.Tensor: """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)""" # Hack to make sure that other schedulers which copy this function don't break # TODO: Add this logic to the other schedulers if hasattr(self.config, "sigma_min"): sigma_min = self.config.sigma_min else: sigma_min = None if hasattr(self.config, "sigma_max"): sigma_max = self.config.sigma_max else: sigma_max = None sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item() sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
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sigmas = np.array( [ sigma_min + (ppf * (sigma_max - sigma_min)) for ppf in [ scipy.stats.beta.ppf(timestep, alpha, beta) for timestep in 1 - np.linspace(0, 1, num_inference_steps) ] ] ) return sigmas def convert_model_output( self, model_output: torch.Tensor, *args, sample: torch.Tensor = None, **kwargs, ) -> torch.Tensor: """ Convert the model output to the corresponding type the DEIS algorithm needs. Args: model_output (`torch.Tensor`): The direct output from the learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process.
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Returns: `torch.Tensor`: The converted model output. """ timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None) if sample is None: if len(args) > 1: sample = args[1] else: raise ValueError("missing `sample` as a required keyward argument") if timestep is not None: deprecate( "timesteps", "1.0.0", "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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sigma = self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma) if self.config.prediction_type == "epsilon": x0_pred = (sample - sigma_t * model_output) / alpha_t elif self.config.prediction_type == "sample": x0_pred = model_output elif self.config.prediction_type == "v_prediction": x0_pred = alpha_t * sample - sigma_t * model_output elif self.config.prediction_type == "flow_prediction": sigma_t = self.sigmas[self.step_index] x0_pred = sample - sigma_t * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, " "`v_prediction`, or `flow_prediction` for the DEISMultistepScheduler." ) if self.config.thresholding: x0_pred = self._threshold_sample(x0_pred)
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if self.config.algorithm_type == "deis": return (sample - alpha_t * x0_pred) / sigma_t else: raise NotImplementedError("only support log-rho multistep deis now") def deis_first_order_update( self, model_output: torch.Tensor, *args, sample: torch.Tensor = None, **kwargs, ) -> torch.Tensor: """ One step for the first-order DEIS (equivalent to DDIM). Args: model_output (`torch.Tensor`): The direct output from the learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. prev_timestep (`int`): The previous discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process.
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Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ timestep = args[0] if len(args) > 0 else kwargs.pop("timestep", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing `sample` as a required keyward argument") if timestep is not None: deprecate( "timesteps", "1.0.0", "Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index] alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t) alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s) lambda_t = torch.log(alpha_t) - torch.log(sigma_t) lambda_s = torch.log(alpha_s) - torch.log(sigma_s) h = lambda_t - lambda_s if self.config.algorithm_type == "deis": x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output else: raise NotImplementedError("only support log-rho multistep deis now") return x_t
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def multistep_deis_second_order_update( self, model_output_list: List[torch.Tensor], *args, sample: torch.Tensor = None, **kwargs, ) -> torch.Tensor: """ One step for the second-order multistep DEIS. Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process.
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Returns: `torch.Tensor`: The sample tensor at the previous timestep. """ timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing `sample` as a required keyward argument") if timestep_list is not None: deprecate( "timestep_list", "1.0.0", "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) sigma_t, sigma_s0, sigma_s1 = ( self.sigmas[self.step_index + 1], self.sigmas[self.step_index], self.sigmas[self.step_index - 1], ) alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t) alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0) alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1) m0, m1 = model_output_list[-1], model_output_list[-2] rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1 if self.config.algorithm_type == "deis":
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def ind_fn(t, b, c): # Integrate[(log(t) - log(c)) / (log(b) - log(c)), {t}] return t * (-np.log(c) + np.log(t) - 1) / (np.log(b) - np.log(c)) coef1 = ind_fn(rho_t, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s0, rho_s1) coef2 = ind_fn(rho_t, rho_s1, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s0) x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1) return x_t else: raise NotImplementedError("only support log-rho multistep deis now") def multistep_deis_third_order_update( self, model_output_list: List[torch.Tensor], *args, sample: torch.Tensor = None, **kwargs, ) -> torch.Tensor: """ One step for the third-order multistep DEIS.
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Args: model_output_list (`List[torch.Tensor]`): The direct outputs from learned diffusion model at current and latter timesteps. sample (`torch.Tensor`): A current instance of a sample created by diffusion process. Returns: `torch.Tensor`: The sample tensor at the previous timestep. """
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timestep_list = args[0] if len(args) > 0 else kwargs.pop("timestep_list", None) prev_timestep = args[1] if len(args) > 1 else kwargs.pop("prev_timestep", None) if sample is None: if len(args) > 2: sample = args[2] else: raise ValueError(" missing`sample` as a required keyward argument") if timestep_list is not None: deprecate( "timestep_list", "1.0.0", "Passing `timestep_list` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", ) if prev_timestep is not None: deprecate( "prev_timestep", "1.0.0", "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`", )
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sigma_t, sigma_s0, sigma_s1, sigma_s2 = ( self.sigmas[self.step_index + 1], self.sigmas[self.step_index], self.sigmas[self.step_index - 1], self.sigmas[self.step_index - 2], ) alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t) alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0) alpha_s1, sigma_s1 = self._sigma_to_alpha_sigma_t(sigma_s1) alpha_s2, sigma_s2 = self._sigma_to_alpha_sigma_t(sigma_s2) m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3] rho_t, rho_s0, rho_s1, rho_s2 = ( sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1, sigma_s2 / alpha_s2, ) if self.config.algorithm_type == "deis":
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def ind_fn(t, b, c, d): # Integrate[(log(t) - log(c))(log(t) - log(d)) / (log(b) - log(c))(log(b) - log(d)), {t}] numerator = t * ( np.log(c) * (np.log(d) - np.log(t) + 1) - np.log(d) * np.log(t) + np.log(d) + np.log(t) ** 2 - 2 * np.log(t) + 2 ) denominator = (np.log(b) - np.log(c)) * (np.log(b) - np.log(d)) return numerator / denominator coef1 = ind_fn(rho_t, rho_s0, rho_s1, rho_s2) - ind_fn(rho_s0, rho_s0, rho_s1, rho_s2) coef2 = ind_fn(rho_t, rho_s1, rho_s2, rho_s0) - ind_fn(rho_s0, rho_s1, rho_s2, rho_s0) coef3 = ind_fn(rho_t, rho_s2, rho_s0, rho_s1) - ind_fn(rho_s0, rho_s2, rho_s0, rho_s1) x_t = alpha_t * (sample / alpha_s0 + coef1 * m0 + coef2 * m1 + coef3 * m2)
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return x_t else: raise NotImplementedError("only support log-rho multistep deis now") # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.index_for_timestep def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps index_candidates = (schedule_timesteps == timestep).nonzero() if len(index_candidates) == 0: step_index = len(self.timesteps) - 1 # The sigma index that is taken for the **very** first `step` # is always the second index (or the last index if there is only 1) # This way we can ensure we don't accidentally skip a sigma in # case we start in the middle of the denoising schedule (e.g. for image-to-image) elif len(index_candidates) > 1: step_index = index_candidates[1].item() else: step_index = index_candidates[0].item()
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return step_index # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index def _init_step_index(self, timestep): """ Initialize the step_index counter for the scheduler. """ if self.begin_index is None: if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) self._step_index = self.index_for_timestep(timestep) else: self._step_index = self._begin_index def step( self, model_output: torch.Tensor, timestep: Union[int, torch.Tensor], sample: torch.Tensor, return_dict: bool = True, ) -> Union[SchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by reversing the SDE. This function propagates the sample with the multistep DEIS.
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Args: model_output (`torch.Tensor`): The direct output from learned diffusion model. timestep (`int`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. return_dict (`bool`): Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if self.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" )
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