Spaces:
Running
on
Zero
Running
on
Zero
File size: 23,009 Bytes
62c110b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 |
# Copyright 2024 Microsoft and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from dataclasses import dataclass
from typing import Optional, Tuple, Union
import numpy as np
import torch
import torch.nn.functional as F
from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput
from .scheduling_utils import SchedulerMixin
@dataclass
class VQDiffusionSchedulerOutput(BaseOutput):
"""
Output class for the scheduler's step function output.
Args:
prev_sample (`torch.LongTensor` of shape `(batch size, num latent pixels)`):
Computed sample x_{t-1} of previous timestep. `prev_sample` should be used as next model input in the
denoising loop.
"""
prev_sample: torch.LongTensor
def index_to_log_onehot(x: torch.LongTensor, num_classes: int) -> torch.FloatTensor:
"""
Convert batch of vector of class indices into batch of log onehot vectors
Args:
x (`torch.LongTensor` of shape `(batch size, vector length)`):
Batch of class indices
num_classes (`int`):
number of classes to be used for the onehot vectors
Returns:
`torch.FloatTensor` of shape `(batch size, num classes, vector length)`:
Log onehot vectors
"""
x_onehot = F.one_hot(x, num_classes)
x_onehot = x_onehot.permute(0, 2, 1)
log_x = torch.log(x_onehot.float().clamp(min=1e-30))
return log_x
def gumbel_noised(logits: torch.FloatTensor, generator: Optional[torch.Generator]) -> torch.FloatTensor:
"""
Apply gumbel noise to `logits`
"""
uniform = torch.rand(logits.shape, device=logits.device, generator=generator)
gumbel_noise = -torch.log(-torch.log(uniform + 1e-30) + 1e-30)
noised = gumbel_noise + logits
return noised
def alpha_schedules(num_diffusion_timesteps: int, alpha_cum_start=0.99999, alpha_cum_end=0.000009):
"""
Cumulative and non-cumulative alpha schedules.
See section 4.1.
"""
att = (
np.arange(0, num_diffusion_timesteps) / (num_diffusion_timesteps - 1) * (alpha_cum_end - alpha_cum_start)
+ alpha_cum_start
)
att = np.concatenate(([1], att))
at = att[1:] / att[:-1]
att = np.concatenate((att[1:], [1]))
return at, att
def gamma_schedules(num_diffusion_timesteps: int, gamma_cum_start=0.000009, gamma_cum_end=0.99999):
"""
Cumulative and non-cumulative gamma schedules.
See section 4.1.
"""
ctt = (
np.arange(0, num_diffusion_timesteps) / (num_diffusion_timesteps - 1) * (gamma_cum_end - gamma_cum_start)
+ gamma_cum_start
)
ctt = np.concatenate(([0], ctt))
one_minus_ctt = 1 - ctt
one_minus_ct = one_minus_ctt[1:] / one_minus_ctt[:-1]
ct = 1 - one_minus_ct
ctt = np.concatenate((ctt[1:], [0]))
return ct, ctt
class VQDiffusionScheduler(SchedulerMixin, ConfigMixin):
"""
A scheduler for vector quantized diffusion.
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_vec_classes (`int`):
The number of classes of the vector embeddings of the latent pixels. Includes the class for the masked
latent pixel.
num_train_timesteps (`int`, defaults to 100):
The number of diffusion steps to train the model.
alpha_cum_start (`float`, defaults to 0.99999):
The starting cumulative alpha value.
alpha_cum_end (`float`, defaults to 0.00009):
The ending cumulative alpha value.
gamma_cum_start (`float`, defaults to 0.00009):
The starting cumulative gamma value.
gamma_cum_end (`float`, defaults to 0.99999):
The ending cumulative gamma value.
"""
order = 1
@register_to_config
def __init__(
self,
num_vec_classes: int,
num_train_timesteps: int = 100,
alpha_cum_start: float = 0.99999,
alpha_cum_end: float = 0.000009,
gamma_cum_start: float = 0.000009,
gamma_cum_end: float = 0.99999,
):
self.num_embed = num_vec_classes
# By convention, the index for the mask class is the last class index
self.mask_class = self.num_embed - 1
at, att = alpha_schedules(num_train_timesteps, alpha_cum_start=alpha_cum_start, alpha_cum_end=alpha_cum_end)
ct, ctt = gamma_schedules(num_train_timesteps, gamma_cum_start=gamma_cum_start, gamma_cum_end=gamma_cum_end)
num_non_mask_classes = self.num_embed - 1
bt = (1 - at - ct) / num_non_mask_classes
btt = (1 - att - ctt) / num_non_mask_classes
at = torch.tensor(at.astype("float64"))
bt = torch.tensor(bt.astype("float64"))
ct = torch.tensor(ct.astype("float64"))
log_at = torch.log(at)
log_bt = torch.log(bt)
log_ct = torch.log(ct)
att = torch.tensor(att.astype("float64"))
btt = torch.tensor(btt.astype("float64"))
ctt = torch.tensor(ctt.astype("float64"))
log_cumprod_at = torch.log(att)
log_cumprod_bt = torch.log(btt)
log_cumprod_ct = torch.log(ctt)
self.log_at = log_at.float()
self.log_bt = log_bt.float()
self.log_ct = log_ct.float()
self.log_cumprod_at = log_cumprod_at.float()
self.log_cumprod_bt = log_cumprod_bt.float()
self.log_cumprod_ct = log_cumprod_ct.float()
# setable values
self.num_inference_steps = None
self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())
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 and diffusion process parameters (alpha, beta, gamma) should be moved
to.
"""
self.num_inference_steps = num_inference_steps
timesteps = np.arange(0, self.num_inference_steps)[::-1].copy()
self.timesteps = torch.from_numpy(timesteps).to(device)
self.log_at = self.log_at.to(device)
self.log_bt = self.log_bt.to(device)
self.log_ct = self.log_ct.to(device)
self.log_cumprod_at = self.log_cumprod_at.to(device)
self.log_cumprod_bt = self.log_cumprod_bt.to(device)
self.log_cumprod_ct = self.log_cumprod_ct.to(device)
def step(
self,
model_output: torch.FloatTensor,
timestep: torch.long,
sample: torch.LongTensor,
generator: Optional[torch.Generator] = None,
return_dict: bool = True,
) -> Union[VQDiffusionSchedulerOutput, Tuple]:
"""
Predict the sample from the previous timestep by the reverse transition distribution. See
[`~VQDiffusionScheduler.q_posterior`] for more details about how the distribution is computer.
Args:
log_p_x_0: (`torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`):
The log probabilities for the predicted classes of the initial latent pixels. Does not include a
prediction for the masked class as the initial unnoised image cannot be masked.
t (`torch.long`):
The timestep that determines which transition matrices are used.
x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`):
The classes of each latent pixel at time `t`.
generator (`torch.Generator`, or `None`):
A random number generator for the noise applied to `p(x_{t-1} | x_t)` before it is sampled from.
return_dict (`bool`, *optional*, defaults to `True`):
Whether or not to return a [`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] or
`tuple`.
Returns:
[`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] is
returned, otherwise a tuple is returned where the first element is the sample tensor.
"""
if timestep == 0:
log_p_x_t_min_1 = model_output
else:
log_p_x_t_min_1 = self.q_posterior(model_output, sample, timestep)
log_p_x_t_min_1 = gumbel_noised(log_p_x_t_min_1, generator)
x_t_min_1 = log_p_x_t_min_1.argmax(dim=1)
if not return_dict:
return (x_t_min_1,)
return VQDiffusionSchedulerOutput(prev_sample=x_t_min_1)
def q_posterior(self, log_p_x_0, x_t, t):
"""
Calculates the log probabilities for the predicted classes of the image at timestep `t-1`:
```
p(x_{t-1} | x_t) = sum( q(x_t | x_{t-1}) * q(x_{t-1} | x_0) * p(x_0) / q(x_t | x_0) )
```
Args:
log_p_x_0 (`torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`):
The log probabilities for the predicted classes of the initial latent pixels. Does not include a
prediction for the masked class as the initial unnoised image cannot be masked.
x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`):
The classes of each latent pixel at time `t`.
t (`torch.Long`):
The timestep that determines which transition matrix is used.
Returns:
`torch.FloatTensor` of shape `(batch size, num classes, num latent pixels)`:
The log probabilities for the predicted classes of the image at timestep `t-1`.
"""
log_onehot_x_t = index_to_log_onehot(x_t, self.num_embed)
log_q_x_t_given_x_0 = self.log_Q_t_transitioning_to_known_class(
t=t, x_t=x_t, log_onehot_x_t=log_onehot_x_t, cumulative=True
)
log_q_t_given_x_t_min_1 = self.log_Q_t_transitioning_to_known_class(
t=t, x_t=x_t, log_onehot_x_t=log_onehot_x_t, cumulative=False
)
# p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) ... p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0)
# . . .
# . . .
# . . .
# p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) ... p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1})
q = log_p_x_0 - log_q_x_t_given_x_0
# sum_0 = p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) + ... + p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}), ... ,
# sum_n = p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) + ... + p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1})
q_log_sum_exp = torch.logsumexp(q, dim=1, keepdim=True)
# p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0 ... p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n
# . . .
# . . .
# . . .
# p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0 ... p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n
q = q - q_log_sum_exp
# (p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1} ... (p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}
# . . .
# . . .
# . . .
# (p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1} ... (p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}
# c_cumulative_{t-1} ... c_cumulative_{t-1}
q = self.apply_cumulative_transitions(q, t - 1)
# ((p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_0) * sum_0 ... ((p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_0) * sum_n
# . . .
# . . .
# . . .
# ((p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_{k-1}) * sum_0 ... ((p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_{k-1}) * sum_n
# c_cumulative_{t-1} * q(x_t | x_{t-1}=C_k) * sum_0 ... c_cumulative_{t-1} * q(x_t | x_{t-1}=C_k) * sum_0
log_p_x_t_min_1 = q + log_q_t_given_x_t_min_1 + q_log_sum_exp
# For each column, there are two possible cases.
#
# Where:
# - sum(p_n(x_0))) is summing over all classes for x_0
# - C_i is the class transitioning from (not to be confused with c_t and c_cumulative_t being used for gamma's)
# - C_j is the class transitioning to
#
# 1. x_t is masked i.e. x_t = c_k
#
# Simplifying the expression, the column vector is:
# .
# .
# .
# (c_t / c_cumulative_t) * (a_cumulative_{t-1} * p_n(x_0 = C_i | x_t) + b_cumulative_{t-1} * sum(p_n(x_0)))
# .
# .
# .
# (c_cumulative_{t-1} / c_cumulative_t) * sum(p_n(x_0))
#
# From equation (11) stated in terms of forward probabilities, the last row is trivially verified.
#
# For the other rows, we can state the equation as ...
#
# (c_t / c_cumulative_t) * [b_cumulative_{t-1} * p(x_0=c_0) + ... + (a_cumulative_{t-1} + b_cumulative_{t-1}) * p(x_0=C_i) + ... + b_cumulative_{k-1} * p(x_0=c_{k-1})]
#
# This verifies the other rows.
#
# 2. x_t is not masked
#
# Simplifying the expression, there are two cases for the rows of the column vector, where C_j = C_i and where C_j != C_i:
# .
# .
# .
# C_j != C_i: b_t * ((b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_0) + ... + ((a_cumulative_{t-1} + b_cumulative_{t-1}) / b_cumulative_t) * p_n(x_0 = C_i) + ... + (b_cumulative_{t-1} / (a_cumulative_t + b_cumulative_t)) * p_n(c_0=C_j) + ... + (b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_{k-1}))
# .
# .
# .
# C_j = C_i: (a_t + b_t) * ((b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_0) + ... + ((a_cumulative_{t-1} + b_cumulative_{t-1}) / (a_cumulative_t + b_cumulative_t)) * p_n(x_0 = C_i = C_j) + ... + (b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_{k-1}))
# .
# .
# .
# 0
#
# The last row is trivially verified. The other rows can be verified by directly expanding equation (11) stated in terms of forward probabilities.
return log_p_x_t_min_1
def log_Q_t_transitioning_to_known_class(
self, *, t: torch.int, x_t: torch.LongTensor, log_onehot_x_t: torch.FloatTensor, cumulative: bool
):
"""
Calculates the log probabilities of the rows from the (cumulative or non-cumulative) transition matrix for each
latent pixel in `x_t`.
Args:
t (`torch.Long`):
The timestep that determines which transition matrix is used.
x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`):
The classes of each latent pixel at time `t`.
log_onehot_x_t (`torch.FloatTensor` of shape `(batch size, num classes, num latent pixels)`):
The log one-hot vectors of `x_t`.
cumulative (`bool`):
If cumulative is `False`, the single step transition matrix `t-1`->`t` is used. If cumulative is
`True`, the cumulative transition matrix `0`->`t` is used.
Returns:
`torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`:
Each _column_ of the returned matrix is a _row_ of log probabilities of the complete probability
transition matrix.
When non cumulative, returns `self.num_classes - 1` rows because the initial latent pixel cannot be
masked.
Where:
- `q_n` is the probability distribution for the forward process of the `n`th latent pixel.
- C_0 is a class of a latent pixel embedding
- C_k is the class of the masked latent pixel
non-cumulative result (omitting logarithms):
```
q_0(x_t | x_{t-1} = C_0) ... q_n(x_t | x_{t-1} = C_0)
. . .
. . .
. . .
q_0(x_t | x_{t-1} = C_k) ... q_n(x_t | x_{t-1} = C_k)
```
cumulative result (omitting logarithms):
```
q_0_cumulative(x_t | x_0 = C_0) ... q_n_cumulative(x_t | x_0 = C_0)
. . .
. . .
. . .
q_0_cumulative(x_t | x_0 = C_{k-1}) ... q_n_cumulative(x_t | x_0 = C_{k-1})
```
"""
if cumulative:
a = self.log_cumprod_at[t]
b = self.log_cumprod_bt[t]
c = self.log_cumprod_ct[t]
else:
a = self.log_at[t]
b = self.log_bt[t]
c = self.log_ct[t]
if not cumulative:
# The values in the onehot vector can also be used as the logprobs for transitioning
# from masked latent pixels. If we are not calculating the cumulative transitions,
# we need to save these vectors to be re-appended to the final matrix so the values
# aren't overwritten.
#
# `P(x_t!=mask|x_{t-1=mask}) = 0` and 0 will be the value of the last row of the onehot vector
# if x_t is not masked
#
# `P(x_t=mask|x_{t-1=mask}) = 1` and 1 will be the value of the last row of the onehot vector
# if x_t is masked
log_onehot_x_t_transitioning_from_masked = log_onehot_x_t[:, -1, :].unsqueeze(1)
# `index_to_log_onehot` will add onehot vectors for masked pixels,
# so the default one hot matrix has one too many rows. See the doc string
# for an explanation of the dimensionality of the returned matrix.
log_onehot_x_t = log_onehot_x_t[:, :-1, :]
# this is a cheeky trick to produce the transition probabilities using log one-hot vectors.
#
# Don't worry about what values this sets in the columns that mark transitions
# to masked latent pixels. They are overwrote later with the `mask_class_mask`.
#
# Looking at the below logspace formula in non-logspace, each value will evaluate to either
# `1 * a + b = a + b` where `log_Q_t` has the one hot value in the column
# or
# `0 * a + b = b` where `log_Q_t` has the 0 values in the column.
#
# See equation 7 for more details.
log_Q_t = (log_onehot_x_t + a).logaddexp(b)
# The whole column of each masked pixel is `c`
mask_class_mask = x_t == self.mask_class
mask_class_mask = mask_class_mask.unsqueeze(1).expand(-1, self.num_embed - 1, -1)
log_Q_t[mask_class_mask] = c
if not cumulative:
log_Q_t = torch.cat((log_Q_t, log_onehot_x_t_transitioning_from_masked), dim=1)
return log_Q_t
def apply_cumulative_transitions(self, q, t):
bsz = q.shape[0]
a = self.log_cumprod_at[t]
b = self.log_cumprod_bt[t]
c = self.log_cumprod_ct[t]
num_latent_pixels = q.shape[2]
c = c.expand(bsz, 1, num_latent_pixels)
q = (q + a).logaddexp(b)
q = torch.cat((q, c), dim=1)
return q
|