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DPM-Solver is designed to discretize an integral of the noise prediction model, and DPM-Solver++ is designed to discretize an integral of the data prediction model. So we need to first convert the model output to the corresponding type to match the algorithm. Note that the algorithm type and the model type is decoupled. That is to say, we can use either DPM-Solver or DPM-Solver++ for both noise prediction model and data prediction model. Args: model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process.
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Returns: `jnp.ndarray`: the converted model output. """ # DPM-Solver++ needs to solve an integral of the data prediction model. if self.config.algorithm_type == "dpmsolver++": if self.config.prediction_type == "epsilon": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] 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": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] x0_pred = alpha_t * sample - sigma_t * model_output else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, " " or `v_prediction` for the FlaxDPMSolverMultistepScheduler." )
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if self.config.thresholding: # Dynamic thresholding in https://arxiv.org/abs/2205.11487 dynamic_max_val = jnp.percentile( jnp.abs(x0_pred), self.config.dynamic_thresholding_ratio, axis=tuple(range(1, x0_pred.ndim)) ) dynamic_max_val = jnp.maximum( dynamic_max_val, self.config.sample_max_value * jnp.ones_like(dynamic_max_val) ) x0_pred = jnp.clip(x0_pred, -dynamic_max_val, dynamic_max_val) / dynamic_max_val return x0_pred # DPM-Solver needs to solve an integral of the noise prediction model. elif self.config.algorithm_type == "dpmsolver": if self.config.prediction_type == "epsilon": return model_output elif self.config.prediction_type == "sample": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep]
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epsilon = (sample - alpha_t * model_output) / sigma_t return epsilon elif self.config.prediction_type == "v_prediction": alpha_t, sigma_t = state.alpha_t[timestep], state.sigma_t[timestep] epsilon = alpha_t * model_output + sigma_t * sample return epsilon else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, " " or `v_prediction` for the FlaxDPMSolverMultistepScheduler." )
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def dpm_solver_first_order_update( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the first-order DPM-Solver (equivalent to DDIM). See https://arxiv.org/abs/2206.00927 for the detailed derivation. Args: model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process.
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Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0 = prev_timestep, timestep m0 = model_output lambda_t, lambda_s = state.lambda_t[t], state.lambda_t[s0] alpha_t, alpha_s = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s = state.sigma_t[t], state.sigma_t[s0] h = lambda_t - lambda_s if self.config.algorithm_type == "dpmsolver++": x_t = (sigma_t / sigma_s) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * m0 elif self.config.algorithm_type == "dpmsolver": x_t = (alpha_t / alpha_s) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * m0 return x_t
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def multistep_dpm_solver_second_order_update( self, state: DPMSolverMultistepSchedulerState, model_output_list: jnp.ndarray, timestep_list: List[int], prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the second-order multistep DPM-Solver. Args: model_output_list (`List[jnp.ndarray]`): direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process.
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Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2] m0, m1 = model_output_list[-1], model_output_list[-2] lambda_t, lambda_s0, lambda_s1 = state.lambda_t[t], state.lambda_t[s0], state.lambda_t[s1] alpha_t, alpha_s0 = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s0 = state.sigma_t[t], state.sigma_t[s0] h, h_0 = lambda_t - lambda_s0, lambda_s0 - lambda_s1 r0 = h_0 / h D0, D1 = m0, (1.0 / r0) * (m0 - m1) if self.config.algorithm_type == "dpmsolver++": # See https://arxiv.org/abs/2211.01095 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 - 0.5 * (alpha_t * (jnp.exp(-h) - 1.0)) * D1 )
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elif self.config.solver_type == "heun": x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 + (alpha_t * ((jnp.exp(-h) - 1.0) / h + 1.0)) * D1 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations if self.config.solver_type == "midpoint": x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - 0.5 * (sigma_t * (jnp.exp(h) - 1.0)) * D1 ) elif self.config.solver_type == "heun": x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - (sigma_t * ((jnp.exp(h) - 1.0) / h - 1.0)) * D1 ) return x_t
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def multistep_dpm_solver_third_order_update( self, state: DPMSolverMultistepSchedulerState, model_output_list: jnp.ndarray, timestep_list: List[int], prev_timestep: int, sample: jnp.ndarray, ) -> jnp.ndarray: """ One step for the third-order multistep DPM-Solver. Args: model_output_list (`List[jnp.ndarray]`): direct outputs from learned diffusion model at current and latter timesteps. timestep (`int`): current and latter discrete timestep in the diffusion chain. prev_timestep (`int`): previous discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process.
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Returns: `jnp.ndarray`: the sample tensor at the previous timestep. """ t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3] m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3] lambda_t, lambda_s0, lambda_s1, lambda_s2 = ( state.lambda_t[t], state.lambda_t[s0], state.lambda_t[s1], state.lambda_t[s2], ) alpha_t, alpha_s0 = state.alpha_t[t], state.alpha_t[s0] sigma_t, sigma_s0 = state.sigma_t[t], state.sigma_t[s0] h, h_0, h_1 = lambda_t - lambda_s0, lambda_s0 - lambda_s1, lambda_s1 - lambda_s2 r0, r1 = h_0 / h, h_1 / h D0 = m0 D1_0, D1_1 = (1.0 / r0) * (m0 - m1), (1.0 / r1) * (m1 - m2) D1 = D1_0 + (r0 / (r0 + r1)) * (D1_0 - D1_1) D2 = (1.0 / (r0 + r1)) * (D1_0 - D1_1) if self.config.algorithm_type == "dpmsolver++":
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# See https://arxiv.org/abs/2206.00927 for detailed derivations x_t = ( (sigma_t / sigma_s0) * sample - (alpha_t * (jnp.exp(-h) - 1.0)) * D0 + (alpha_t * ((jnp.exp(-h) - 1.0) / h + 1.0)) * D1 - (alpha_t * ((jnp.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2 ) elif self.config.algorithm_type == "dpmsolver": # See https://arxiv.org/abs/2206.00927 for detailed derivations x_t = ( (alpha_t / alpha_s0) * sample - (sigma_t * (jnp.exp(h) - 1.0)) * D0 - (sigma_t * ((jnp.exp(h) - 1.0) / h - 1.0)) * D1 - (sigma_t * ((jnp.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2 ) return x_t
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def step( self, state: DPMSolverMultistepSchedulerState, model_output: jnp.ndarray, timestep: int, sample: jnp.ndarray, return_dict: bool = True, ) -> Union[FlaxDPMSolverMultistepSchedulerOutput, Tuple]: """ Predict the sample at the previous timestep by DPM-Solver. Core function to propagate the diffusion process from the learned model outputs (most often the predicted noise). Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. model_output (`jnp.ndarray`): direct output from learned diffusion model. timestep (`int`): current discrete timestep in the diffusion chain. sample (`jnp.ndarray`): current instance of sample being created by diffusion process. return_dict (`bool`): option for returning tuple rather than FlaxDPMSolverMultistepSchedulerOutput class
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Returns: [`FlaxDPMSolverMultistepSchedulerOutput`] or `tuple`: [`FlaxDPMSolverMultistepSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When returning a tuple, the first element is the sample tensor. """ if state.num_inference_steps is None: raise ValueError( "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler" ) (step_index,) = jnp.where(state.timesteps == timestep, size=1) step_index = step_index[0] prev_timestep = jax.lax.select(step_index == len(state.timesteps) - 1, 0, state.timesteps[step_index + 1]) model_output = self.convert_model_output(state, model_output, timestep, sample)
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model_outputs_new = jnp.roll(state.model_outputs, -1, axis=0) model_outputs_new = model_outputs_new.at[-1].set(model_output) state = state.replace( model_outputs=model_outputs_new, prev_timestep=prev_timestep, cur_sample=sample, ) def step_1(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: return self.dpm_solver_first_order_update( state, state.model_outputs[-1], state.timesteps[step_index], state.prev_timestep, state.cur_sample, )
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def step_23(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: def step_2(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: timestep_list = jnp.array([state.timesteps[step_index - 1], state.timesteps[step_index]]) return self.multistep_dpm_solver_second_order_update( state, state.model_outputs, timestep_list, state.prev_timestep, state.cur_sample, )
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def step_3(state: DPMSolverMultistepSchedulerState) -> jnp.ndarray: timestep_list = jnp.array( [ state.timesteps[step_index - 2], state.timesteps[step_index - 1], state.timesteps[step_index], ] ) return self.multistep_dpm_solver_third_order_update( state, state.model_outputs, timestep_list, state.prev_timestep, state.cur_sample, ) step_2_output = step_2(state) step_3_output = step_3(state)
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if self.config.solver_order == 2: return step_2_output elif self.config.lower_order_final and len(state.timesteps) < 15: return jax.lax.select( state.lower_order_nums < 2, step_2_output, jax.lax.select( step_index == len(state.timesteps) - 2, step_2_output, step_3_output, ), ) else: return jax.lax.select( state.lower_order_nums < 2, step_2_output, step_3_output, ) step_1_output = step_1(state) step_23_output = step_23(state) if self.config.solver_order == 1: prev_sample = step_1_output
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elif self.config.lower_order_final and len(state.timesteps) < 15: prev_sample = jax.lax.select( state.lower_order_nums < 1, step_1_output, jax.lax.select( step_index == len(state.timesteps) - 1, step_1_output, step_23_output, ), ) else: prev_sample = jax.lax.select( state.lower_order_nums < 1, step_1_output, step_23_output, ) state = state.replace( lower_order_nums=jnp.minimum(state.lower_order_nums + 1, self.config.solver_order), ) if not return_dict: return (prev_sample, state) return FlaxDPMSolverMultistepSchedulerOutput(prev_sample=prev_sample, state=state)
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def scale_model_input( self, state: DPMSolverMultistepSchedulerState, sample: jnp.ndarray, timestep: Optional[int] = None ) -> jnp.ndarray: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Args: state (`DPMSolverMultistepSchedulerState`): the `FlaxDPMSolverMultistepScheduler` state data class instance. sample (`jnp.ndarray`): input sample timestep (`int`, optional): current timestep Returns: `jnp.ndarray`: scaled input sample """ return sample def add_noise( self, state: DPMSolverMultistepSchedulerState, original_samples: jnp.ndarray, noise: jnp.ndarray, timesteps: jnp.ndarray, ) -> jnp.ndarray: return add_noise_common(state.common, original_samples, noise, timesteps) def __len__(self): return self.config.num_train_timesteps
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class DDIMSchedulerOutput(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. pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.Tensor pred_original_sample: Optional[torch.Tensor] = None
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class CogVideoXDDIMScheduler(SchedulerMixin, ConfigMixin): """ `DDIMScheduler` extends the denoising procedure introduced in denoising diffusion probabilistic models (DDPMs) with non-Markovian guidance. 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`. clip_sample (`bool`, defaults to `True`): Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=True`. set_alpha_to_one (`bool`, defaults to `True`):
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Each diffusion step uses the alphas product value at that step and at the previous one. For the final step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`, otherwise it uses the alpha value at step 0. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. prediction_type (`str`, defaults to `epsilon`, *optional*): 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.
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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`. timestep_spacing (`str`, defaults to `"leading"`): 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. rescale_betas_zero_snr (`bool`, defaults to `False`): Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to
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[`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """
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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 = 0.00085, beta_end: float = 0.0120, beta_schedule: str = "scaled_linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, clip_sample: bool = True, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", clip_sample_range: float = 1.0, sample_max_value: float = 1.0, timestep_spacing: str = "leading", rescale_betas_zero_snr: bool = False, snr_shift_scale: float = 3.0, ): 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":
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# 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.float64) ** 2 elif beta_schedule == "squaredcos_cap_v2": # Glide cosine schedule 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) # Modify: SNR shift following SD3 self.alphas_cumprod = self.alphas_cumprod / (snr_shift_scale + (1 - snr_shift_scale) * self.alphas_cumprod) # Rescale for zero SNR if rescale_betas_zero_snr: self.alphas_cumprod = rescale_zero_terminal_snr(self.alphas_cumprod) # At every step in ddim, we are looking into the previous alphas_cumprod # For the final step, there is no previous alphas_cumprod because we are already at 0 # `set_alpha_to_one` decides whether we set this parameter simply to one or # whether we use the final alpha of the "non-previous" one. self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0] # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0
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# setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64)) def _get_variance(self, timestep, prev_timestep): alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance 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`): The input sample. timestep (`int`, *optional*): The current timestep in the diffusion chain. Returns: `torch.Tensor`: A scaled input sample. """ return sample 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). Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. """
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if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." ) self.num_inference_steps = num_inference_steps
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# "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) .round()[::-1] .copy() .astype(np.int64) ) elif self.config.timestep_spacing == "leading": step_ratio = self.config.num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.int64) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / self.num_inference_steps
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# creates integer timesteps by multiplying by ratio # casting to int to avoid issues when num_inference_step is power of 3 timesteps = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64) timesteps -= 1 else: raise ValueError( f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'." )
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self.timesteps = torch.from_numpy(timesteps).to(device) def step( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, eta: float = 0.0, use_clipped_model_output: bool = False, generator=None, variance_noise: Optional[torch.Tensor] = None, return_dict: bool = True, ) -> Union[DDIMSchedulerOutput, 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 (`float`): The current discrete timestep in the diffusion chain. sample (`torch.Tensor`): A current instance of a sample created by the diffusion process. eta (`float`): The weight of noise for added noise in diffusion step. use_clipped_model_output (`bool`, defaults to `False`): If `True`, computes "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` has no effect. generator (`torch.Generator`, *optional*): A random number generator.
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variance_noise (`torch.Tensor`): Alternative to generating noise with `generator` by directly providing the noise for the variance itself. Useful for methods such as [`CycleDiffusion`]. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.
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Returns: [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] 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" ) # 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"
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# 1. get previous step value (=t-1) prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps # 2. compute alphas, betas alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod 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 # To make style tests pass, commented out `pred_epsilon` as it is an unused variable 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(
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f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or" " `v_prediction`" )
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a_t = ((1 - alpha_prod_t_prev) / (1 - alpha_prod_t)) ** 0.5 b_t = alpha_prod_t_prev**0.5 - alpha_prod_t**0.5 * a_t prev_sample = a_t * sample + b_t * pred_original_sample if not return_dict: return ( prev_sample, pred_original_sample, ) return DDIMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_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 TCDSchedulerOutput(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. pred_noised_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted noised sample `(x_{s})` based on the model output from the current timestep. """ prev_sample: torch.Tensor pred_noised_sample: Optional[torch.Tensor] = None
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class TCDScheduler(SchedulerMixin, ConfigMixin): """ `TCDScheduler` incorporates the `Strategic Stochastic Sampling` introduced by the paper `Trajectory Consistency Distillation`, extending the original Multistep Consistency Sampling to enable unrestricted trajectory traversal. This code is based on the official repo of TCD(https://github.com/jabir-zheng/TCD). This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. [`~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.
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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`. original_inference_steps (`int`, *optional*, defaults to 50): The default number of inference steps used to generate a linearly-spaced timestep schedule, from which we will ultimately take `num_inference_steps` evenly spaced timesteps to form the final timestep schedule.
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clip_sample (`bool`, defaults to `True`): Clip the predicted sample for numerical stability. clip_sample_range (`float`, defaults to 1.0): The maximum magnitude for sample clipping. Valid only when `clip_sample=True`. set_alpha_to_one (`bool`, defaults to `True`): Each diffusion step uses the alphas product value at that step and at the previous one. For the final step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`, otherwise it uses the alpha value at step 0. steps_offset (`int`, defaults to 0): An offset added to the inference steps, as required by some model families. prediction_type (`str`, defaults to `epsilon`, *optional*): Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
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`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`. timestep_spacing (`str`, defaults to `"leading"`): 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. timestep_scaling (`float`, defaults to 10.0):
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The factor the timesteps will be multiplied by when calculating the consistency model boundary conditions `c_skip` and `c_out`. Increasing this will decrease the approximation error (although the approximation error at the default of `10.0` is already pretty small). rescale_betas_zero_snr (`bool`, defaults to `False`): Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """
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order = 1
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@register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.00085, beta_end: float = 0.012, beta_schedule: str = "scaled_linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, original_inference_steps: int = 50, clip_sample: bool = False, clip_sample_range: float = 1.0, set_alpha_to_one: bool = True, steps_offset: int = 0, prediction_type: str = "epsilon", thresholding: bool = False, dynamic_thresholding_ratio: float = 0.995, sample_max_value: float = 1.0, timestep_spacing: str = "leading", timestep_scaling: float = 10.0, rescale_betas_zero_snr: bool = False, ): if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear":
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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 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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# Rescale for zero SNR if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) # At every step in ddim, we are looking into the previous alphas_cumprod # For the final step, there is no previous alphas_cumprod because we are already at 0 # `set_alpha_to_one` decides whether we set this parameter simply to one or # whether we use the final alpha of the "non-previous" one. self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0] # standard deviation of the initial noise distribution self.init_noise_sigma = 1.0 # setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64)) self.custom_timesteps = False
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self._step_index = None self._begin_index = None # 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 @property def step_index(self): 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 # 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.
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Args: begin_index (`int`): The begin index for the scheduler. """ self._begin_index = begin_index 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. Returns: `torch.Tensor`: A scaled input sample. """ return sample
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# Copied from diffusers.schedulers.scheduling_ddim.DDIMScheduler._get_variance def _get_variance(self, timestep, prev_timestep): alpha_prod_t = self.alphas_cumprod[timestep] alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod beta_prod_t = 1 - alpha_prod_t beta_prod_t_prev = 1 - alpha_prod_t_prev variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev) return variance
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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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def set_timesteps( self, num_inference_steps: Optional[int] = None, device: Union[str, torch.device] = None, original_inference_steps: Optional[int] = None, timesteps: Optional[List[int]] = None, strength: float = 1.0, ): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference).
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Args: num_inference_steps (`int`, *optional*): The number of diffusion steps used when generating samples with a pre-trained model. If used, `timesteps` must be `None`. device (`str` or `torch.device`, *optional*): The device to which the timesteps should be moved to. If `None`, the timesteps are not moved. original_inference_steps (`int`, *optional*): The original number of inference steps, which will be used to generate a linearly-spaced timestep schedule (which is different from the standard `diffusers` implementation). We will then take `num_inference_steps` timesteps from this schedule, evenly spaced in terms of indices, and use that as our final timestep schedule. If not set, this will default to the `original_inference_steps` attribute. timesteps (`List[int]`, *optional*):
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Custom timesteps used to support arbitrary spacing between timesteps. If `None`, then the default timestep spacing strategy of equal spacing between timesteps on the training/distillation timestep schedule is used. If `timesteps` is passed, `num_inference_steps` must be `None`. strength (`float`, *optional*, defaults to 1.0): Used to determine the number of timesteps used for inference when using img2img, inpaint, etc. """ # 0. Check inputs if num_inference_steps is None and timesteps is None: raise ValueError("Must pass exactly one of `num_inference_steps` or `custom_timesteps`.")
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if num_inference_steps is not None and timesteps is not None: raise ValueError("Can only pass one of `num_inference_steps` or `custom_timesteps`.") # 1. Calculate the TCD original training/distillation timestep schedule. original_steps = ( original_inference_steps if original_inference_steps is not None else self.config.original_inference_steps )
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if original_inference_steps is None: # default option, timesteps align with discrete inference steps if original_steps > self.config.num_train_timesteps: raise ValueError( f"`original_steps`: {original_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." ) # TCD Timesteps Setting # The skipping step parameter k from the paper. k = self.config.num_train_timesteps // original_steps # TCD Training/Distillation Steps Schedule tcd_origin_timesteps = np.asarray(list(range(1, int(original_steps * strength) + 1))) * k - 1 else: # customised option, sampled timesteps can be any arbitrary value
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tcd_origin_timesteps = np.asarray(list(range(0, int(self.config.num_train_timesteps * strength))))
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# 2. Calculate the TCD inference timestep schedule. if timesteps is not None: # 2.1 Handle custom timestep schedules. train_timesteps = set(tcd_origin_timesteps) non_train_timesteps = [] for i in range(1, len(timesteps)): if timesteps[i] >= timesteps[i - 1]: raise ValueError("`custom_timesteps` must be in descending order.") if timesteps[i] not in train_timesteps: non_train_timesteps.append(timesteps[i]) if timesteps[0] >= self.config.num_train_timesteps: raise ValueError( f"`timesteps` must start before `self.config.train_timesteps`:" f" {self.config.num_train_timesteps}." )
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# Raise warning if timestep schedule does not start with self.config.num_train_timesteps - 1 if strength == 1.0 and timesteps[0] != self.config.num_train_timesteps - 1: logger.warning( f"The first timestep on the custom timestep schedule is {timesteps[0]}, not" f" `self.config.num_train_timesteps - 1`: {self.config.num_train_timesteps - 1}. You may get" f" unexpected results when using this timestep schedule." ) # Raise warning if custom timestep schedule contains timesteps not on original timestep schedule if non_train_timesteps: logger.warning( f"The custom timestep schedule contains the following timesteps which are not on the original" f" training/distillation timestep schedule: {non_train_timesteps}. You may get unexpected results" f" when using this timestep schedule." )
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# Raise warning if custom timestep schedule is longer than original_steps if original_steps is not None: if len(timesteps) > original_steps: logger.warning( f"The number of timesteps in the custom timestep schedule is {len(timesteps)}, which exceeds the" f" the length of the timestep schedule used for training: {original_steps}. You may get some" f" unexpected results when using this timestep schedule." ) else: if len(timesteps) > self.config.num_train_timesteps: logger.warning( f"The number of timesteps in the custom timestep schedule is {len(timesteps)}, which exceeds the" f" the length of the timestep schedule used for training: {self.config.num_train_timesteps}. You may get some" f" unexpected results when using this timestep schedule."
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)
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timesteps = np.array(timesteps, dtype=np.int64) self.num_inference_steps = len(timesteps) self.custom_timesteps = True
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# Apply strength (e.g. for img2img pipelines) (see StableDiffusionImg2ImgPipeline.get_timesteps) init_timestep = min(int(self.num_inference_steps * strength), self.num_inference_steps) t_start = max(self.num_inference_steps - init_timestep, 0) timesteps = timesteps[t_start * self.order :] # TODO: also reset self.num_inference_steps? else: # 2.2 Create the "standard" TCD inference timestep schedule. if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:" f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle" f" maximal {self.config.num_train_timesteps} timesteps." )
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if original_steps is not None: skipping_step = len(tcd_origin_timesteps) // num_inference_steps if skipping_step < 1: raise ValueError( f"The combination of `original_steps x strength`: {original_steps} x {strength} is smaller than `num_inference_steps`: {num_inference_steps}. Make sure to either reduce `num_inference_steps` to a value smaller than {int(original_steps * strength)} or increase `strength` to a value higher than {float(num_inference_steps / original_steps)}." ) self.num_inference_steps = num_inference_steps
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if original_steps is not None: if num_inference_steps > original_steps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `original_inference_steps`:" f" {original_steps} because the final timestep schedule will be a subset of the" f" `original_inference_steps`-sized initial timestep schedule." ) else: if num_inference_steps > self.config.num_train_timesteps: raise ValueError( f"`num_inference_steps`: {num_inference_steps} cannot be larger than `num_train_timesteps`:" f" {self.config.num_train_timesteps} because the final timestep schedule will be a subset of the" f" `num_train_timesteps`-sized initial timestep schedule." )
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# TCD Inference Steps Schedule tcd_origin_timesteps = tcd_origin_timesteps[::-1].copy() # Select (approximately) evenly spaced indices from tcd_origin_timesteps. inference_indices = np.linspace(0, len(tcd_origin_timesteps), num=num_inference_steps, endpoint=False) inference_indices = np.floor(inference_indices).astype(np.int64) timesteps = tcd_origin_timesteps[inference_indices] self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.long) self._step_index = None self._begin_index = None
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def step( self, model_output: torch.Tensor, timestep: int, sample: torch.Tensor, eta: float = 0.3, generator: Optional[torch.Generator] = None, return_dict: bool = True, ) -> Union[TCDSchedulerOutput, 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. eta (`float`): A stochastic parameter (referred to as `gamma` in the paper) used to control the stochasticity in every step. When eta = 0, it represents deterministic sampling, whereas eta = 1 indicates full stochastic sampling. generator (`torch.Generator`, *optional*): A random number generator. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_tcd.TCDSchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_utils.TCDSchedulerOutput`] or `tuple`:
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If return_dict is `True`, [`~schedulers.scheduling_tcd.TCDSchedulerOutput`] 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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if self.step_index is None: self._init_step_index(timestep) assert 0 <= eta <= 1.0, "gamma must be less than or equal to 1.0" # 1. get previous step value prev_step_index = self.step_index + 1 if prev_step_index < len(self.timesteps): prev_timestep = self.timesteps[prev_step_index] else: prev_timestep = torch.tensor(0) timestep_s = torch.floor((1 - eta) * prev_timestep).to(dtype=torch.long) # 2. compute alphas, betas alpha_prod_t = self.alphas_cumprod[timestep] beta_prod_t = 1 - alpha_prod_t alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod alpha_prod_s = self.alphas_cumprod[timestep_s] beta_prod_s = 1 - alpha_prod_s
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# 3. Compute the predicted noised sample x_s based on the model parameterization if self.config.prediction_type == "epsilon": # noise-prediction pred_original_sample = (sample - beta_prod_t.sqrt() * model_output) / alpha_prod_t.sqrt() pred_epsilon = model_output pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon elif self.config.prediction_type == "sample": # x-prediction pred_original_sample = model_output pred_epsilon = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5) pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon elif self.config.prediction_type == "v_prediction": # 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
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pred_noised_sample = alpha_prod_s.sqrt() * pred_original_sample + beta_prod_s.sqrt() * pred_epsilon else: raise ValueError( f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample` or" " `v_prediction` for `TCDScheduler`." )
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# 4. Sample and inject noise z ~ N(0, I) for MultiStep Inference # Noise is not used on the final timestep of the timestep schedule. # This also means that noise is not used for one-step sampling. # Eta (referred to as "gamma" in the paper) was introduced to control the stochasticity in every step. # When eta = 0, it represents deterministic sampling, whereas eta = 1 indicates full stochastic sampling. if eta > 0: if self.step_index != self.num_inference_steps - 1: noise = randn_tensor( model_output.shape, generator=generator, device=model_output.device, dtype=pred_noised_sample.dtype ) prev_sample = (alpha_prod_t_prev / alpha_prod_s).sqrt() * pred_noised_sample + ( 1 - alpha_prod_t_prev / alpha_prod_s ).sqrt() * noise else: prev_sample = pred_noised_sample else: prev_sample = pred_noised_sample
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# upon completion increase step index by one self._step_index += 1 if not return_dict: return (prev_sample, pred_noised_sample) return TCDSchedulerOutput(prev_sample=prev_sample, pred_noised_sample=pred_noised_sample) # 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)
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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(original_samples.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(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
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# 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) 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)
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velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample return velocity def __len__(self): return self.config.num_train_timesteps # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.previous_timestep def previous_timestep(self, timestep): if self.custom_timesteps or self.num_inference_steps: index = (self.timesteps == timestep).nonzero(as_tuple=True)[0][0] if index == self.timesteps.shape[0] - 1: prev_t = torch.tensor(-1) else: prev_t = self.timesteps[index + 1] else: prev_t = timestep - 1 return prev_t
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class EulerAncestralDiscreteSchedulerOutput(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. pred_original_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images): The predicted denoised sample `(x_{0})` based on the model output from the current timestep. `pred_original_sample` can be used to preview progress or for guidance. """ prev_sample: torch.Tensor pred_original_sample: Optional[torch.Tensor] = None
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class EulerAncestralDiscreteScheduler(SchedulerMixin, ConfigMixin): """ Ancestral sampling with Euler method steps. 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` or `scaled_linear`. trained_betas (`np.ndarray`, *optional*): Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`. prediction_type (`str`, defaults to `epsilon`, *optional*): 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
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Video](https://imagen.research.google/video/paper.pdf) paper). timestep_spacing (`str`, defaults to `"linspace"`): 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. rescale_betas_zero_snr (`bool`, defaults to `False`): Whether to rescale the betas to have zero terminal SNR. This enables the model to generate very bright and dark samples instead of limiting it to samples with medium brightness. Loosely related to [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506). """
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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[Union[np.ndarray, List[float]]] = None, prediction_type: str = "epsilon", timestep_spacing: str = "linspace", steps_offset: int = 0, rescale_betas_zero_snr: bool = False, ): 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":
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# Glide cosine schedule 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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if rescale_betas_zero_snr: self.betas = rescale_zero_terminal_snr(self.betas) self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) if rescale_betas_zero_snr: # Close to 0 without being 0 so first sigma is not inf # FP16 smallest positive subnormal works well here self.alphas_cumprod[-1] = 2**-24 sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32) self.sigmas = torch.from_numpy(sigmas) # setable values self.num_inference_steps = None timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy() self.timesteps = torch.from_numpy(timesteps) self.is_scale_input_called = False
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self._step_index = None self._begin_index = None self.sigmas = self.sigmas.to("cpu") # to avoid too much CPU/GPU communication @property def init_noise_sigma(self): # standard deviation of the initial noise distribution if self.config.timestep_spacing in ["linspace", "trailing"]: return self.sigmas.max() return (self.sigmas.max() ** 2 + 1) ** 0.5 @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 scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.Tensor]) -> torch.Tensor: """ Ensures interchangeability with schedulers that need to scale the denoising model input depending on the current timestep. Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the Euler algorithm. 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. """ if self.step_index is None: self._init_step_index(timestep) sigma = self.sigmas[self.step_index] sample = sample / ((sigma**2 + 1) ** 0.5) self.is_scale_input_called = True return sample 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). 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
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# "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, dtype=np.float32)[ ::-1 ].copy() elif self.config.timestep_spacing == "leading": step_ratio = self.config.num_train_timesteps // self.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(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.float32) timesteps += self.config.steps_offset elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / self.num_inference_steps # creates integer timesteps by multiplying by ratio
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