Spaces:
Running
on
Zero
Running
on
Zero
File size: 49,983 Bytes
11e6f7b |
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 |
"""
This code started out as a PyTorch port of Ho et al's diffusion models:
https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py
Docstrings have been added, as well as DDIM sampling and a new collection of beta schedules.
"""
from pdb import set_trace as st
import enum
import math
import numpy as np
import torch as th
from .nn import mean_flat
from .losses import normal_kl, discretized_gaussian_log_likelihood
from . import dist_util
def get_named_beta_schedule(schedule_name, num_diffusion_timesteps):
"""
Get a pre-defined beta schedule for the given name.
The beta schedule library consists of beta schedules which remain similar
in the limit of num_diffusion_timesteps.
Beta schedules may be added, but should not be removed or changed once
they are committed to maintain backwards compatibility.
"""
if schedule_name == "linear": # * used here
# Linear schedule from Ho et al, extended to work for any number of
# diffusion steps.
scale = 1000 / num_diffusion_timesteps
beta_start = scale * 0.0001
beta_end = scale * 0.02
return np.linspace(beta_start,
beta_end,
num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "linear_simple":
return betas_for_alpha_bar_linear_simple(num_diffusion_timesteps,
lambda t: 0.001 / (1.001 - t))
elif schedule_name == "cosine":
return betas_for_alpha_bar(
num_diffusion_timesteps,
lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2)**2,
)
else:
raise NotImplementedError(f"unknown beta schedule: {schedule_name}")
def betas_for_alpha_bar_linear_simple(num_diffusion_timesteps,
alpha_bar,
max_beta=0.999):
"""proposed by Chen Ting, on the importance of noise schedule, arXiv 2023.
gamma = 1-t
"""
betas = []
for i in range(num_diffusion_timesteps):
t = i / num_diffusion_timesteps
betas.append(min(max_beta, alpha_bar(t)))
return betas
def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):
"""
Create a beta schedule that discretizes the given alpha_t_bar function,
which defines the cumulative product of (1-beta) over time from t = [0,1].
:param num_diffusion_timesteps: the number of betas to produce.
:param alpha_bar: a lambda that takes an argument t from 0 to 1 and
produces the cumulative product of (1-beta) up to that
part of the diffusion process.
:param max_beta: the maximum beta to use; use values lower than 1 to
prevent singularities.
"""
betas = []
for i in range(num_diffusion_timesteps):
t1 = i / num_diffusion_timesteps
t2 = (i + 1) / num_diffusion_timesteps
betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
return np.array(betas)
class ModelMeanType(enum.Enum):
"""
Which type of output the model predicts.
"""
PREVIOUS_X = enum.auto() # the model predicts x_{t-1}
START_X = enum.auto() # the model predicts x_0
EPSILON = enum.auto() # the model predicts epsilon
V = enum.auto() # the model predicts velosity
class ModelVarType(enum.Enum):
"""
What is used as the model's output variance.
The LEARNED_RANGE option has been added to allow the model to predict
values between FIXED_SMALL and FIXED_LARGE, making its job easier.
"""
LEARNED = enum.auto()
FIXED_SMALL = enum.auto()
FIXED_LARGE = enum.auto()
LEARNED_RANGE = enum.auto()
class LossType(enum.Enum):
MSE = enum.auto() # use raw MSE loss (and KL when learning variances)
RESCALED_MSE = (
enum.auto()
) # use raw MSE loss (with RESCALED_KL when learning variances)
KL = enum.auto() # use the variational lower-bound
RESCALED_KL = enum.auto() # like KL, but rescale to estimate the full VLB
def is_vb(self):
return self == LossType.KL or self == LossType.RESCALED_KL
class GaussianDiffusion:
"""
Utilities for training and sampling diffusion models.
Ported directly from here, and then adapted over time to further experimentation.
https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42
:param betas: a 1-D numpy array of betas for each diffusion timestep,
starting at T and going to 1.
:param model_mean_type: a ModelMeanType determining what the model outputs.
:param model_var_type: a ModelVarType determining how variance is output.
:param loss_type: a LossType determining the loss function to use.
:param rescale_timesteps: if True, pass floating point timesteps into the
model so that they are always scaled like in the
original paper (0 to 1000).
"""
'''
defaults:
learn_sigma=False,
diffusion_steps=1000,
noise_schedule="linear",
timestep_respacing="",
use_kl=False,
predict_xstart=False,
rescale_timesteps=False,
rescale_learned_sigmas=False,
'''
def __init__(
self,
*,
betas,
model_mean_type,
model_var_type,
loss_type,
rescale_timesteps=False,
standarization_xt=False,
):
self.model_mean_type = model_mean_type
self.model_var_type = model_var_type
self.loss_type = loss_type
self.rescale_timesteps = rescale_timesteps
self.standarization_xt = standarization_xt
# Use float64 for accuracy.
betas = np.array(betas, dtype=np.float64)
self.betas = betas
assert len(betas.shape) == 1, "betas must be 1-D"
assert (betas > 0).all() and (betas <= 1).all()
self.num_timesteps = int(betas.shape[0])
alphas = 1.0 - betas
self.alphas_cumprod = np.cumprod(alphas, axis=0)
self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1])
self.alphas_cumprod_next = np.append(self.alphas_cumprod[1:], 0.0)
assert self.alphas_cumprod_prev.shape == (self.num_timesteps, )
# calculations for diffusion q(x_t | x_{t-1}) and others
self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod)
self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod)
self.log_one_minus_alphas_cumprod = np.log(1.0 - self.alphas_cumprod)
self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod)
self.sqrt_recipm1_alphas_cumprod = np.sqrt(
1.0 / self.alphas_cumprod -
1) # sqrt(1/cumprod(alphas) - 1), for calculating x_0 from x_t
# calculations for posterior q(x_{t-1} | x_t, x_0)
self.posterior_variance = (betas * (1.0 - self.alphas_cumprod_prev) /
(1.0 - self.alphas_cumprod))
# log calculation clipped because the posterior variance is 0 at the
# beginning of the diffusion chain.
self.posterior_log_variance_clipped = np.log(
np.append(self.posterior_variance[1], self.posterior_variance[1:]))
self.posterior_mean_coef1 = (betas *
np.sqrt(self.alphas_cumprod_prev) /
(1.0 - self.alphas_cumprod))
self.posterior_mean_coef2 = ((1.0 - self.alphas_cumprod_prev) *
np.sqrt(alphas) /
(1.0 - self.alphas_cumprod))
def q_mean_variance(self, x_start, t):
"""
Get the distribution q(x_t | x_0).
:param x_start: the [N x C x ...] tensor of noiseless inputs.
:param t: the number of diffusion steps (minus 1). Here, 0 means one step.
:return: A tuple (mean, variance, log_variance), all of x_start's shape.
"""
mean = (
_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) *
x_start)
variance = _extract_into_tensor(1.0 - self.alphas_cumprod, t,
x_start.shape)
log_variance = _extract_into_tensor(self.log_one_minus_alphas_cumprod,
t, x_start.shape)
return mean, variance, log_variance
def q_sample(self, x_start, t, noise=None, return_detail=False):
"""
Diffuse the data for a given number of diffusion steps.
In other words, sample from q(x_t | x_0).
:param x_start: the initial data batch.
:param t: the number of diffusion steps (minus 1). Here, 0 means one step.
:param noise: if specified, the split-out normal noise.
:return: A noisy version of x_start.
"""
if noise is None:
noise = th.randn_like(x_start)
assert noise.shape == x_start.shape
alpha_bar = _extract_into_tensor(self.sqrt_alphas_cumprod, t,
x_start.shape)
one_minus_alpha_bar = _extract_into_tensor(
self.sqrt_one_minus_alphas_cumprod, t, x_start.shape)
xt = (alpha_bar * x_start + one_minus_alpha_bar * noise)
if self.standarization_xt:
xt = xt / (1e-5 + xt.std(dim=list(range(1, xt.ndim)), keepdim=True)
) # B 1 1 1 #
if return_detail:
return xt, alpha_bar, one_minus_alpha_bar
return xt
def q_posterior_mean_variance(self, x_start, x_t, t):
"""
Compute the mean and variance of the diffusion posterior:
q(x_{t-1} | x_t, x_0)
"""
assert x_start.shape == x_t.shape
posterior_mean = (
_extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) *
x_start +
_extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) *
x_t)
posterior_variance = _extract_into_tensor(self.posterior_variance, t,
x_t.shape)
posterior_log_variance_clipped = _extract_into_tensor(
self.posterior_log_variance_clipped, t, x_t.shape)
assert (posterior_mean.shape[0] == posterior_variance.shape[0] ==
posterior_log_variance_clipped.shape[0] == x_start.shape[0])
return posterior_mean, posterior_variance, posterior_log_variance_clipped
def p_mean_variance(self,
model,
x,
t,
c=None,
clip_denoised=True,
denoised_fn=None,
model_kwargs=None,
mixing_normal=False,
direct_return_model_output=False):
"""
Apply the model to get p(x_{t-1} | x_t), as well as a prediction of
the initial x, x_0.
:param model: the model, which takes a signal and a batch of timesteps
as input.
:param x: the [N x C x ...] tensor at time t.
:param t: a 1-D Tensor of timesteps.
:param clip_denoised: if True, clip the denoised signal into [-1, 1].
:param denoised_fn: if not None, a function which applies to the
x_start prediction before it is used to sample. Applies before
clip_denoised.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:return: a dict with the following keys:
- 'mean': the model mean output.
- 'variance': the model variance output.
- 'log_variance': the log of 'variance'.
- 'pred_xstart': the prediction for x_0.
"""
# lazy import to avoid partially initialized import
from guided_diffusion.continuous_diffusion_utils import get_mixed_prediction
if model_kwargs is None:
model_kwargs = {}
# if mixing_normal is not None:
# t = t / self.num_timesteps # [0,1] for SDE diffusion
B, C = x.shape[:2]
assert t.shape == (B, )
model_output = model(x,
self._scale_timesteps(t),
c=c,
mixing_normal=mixing_normal,
**model_kwargs)
if direct_return_model_output:
return model_output
if self.model_mean_type == ModelMeanType.V:
v_transformed_to_eps_flag = False
# st()
if mixing_normal: # directly change the model predicted eps logits
if self.model_mean_type == ModelMeanType.START_X:
mixing_component = self.get_mixing_component_x0(x,
t,
enabled=True)
else:
assert self.model_mean_type in [
ModelMeanType.EPSILON, ModelMeanType.V
]
mixing_component = self.get_mixing_component(x,
t,
enabled=True)
if self.model_mean_type == ModelMeanType.V:
model_output = self._predict_eps_from_z_and_v(
x, t, model_output)
v_transformed_to_eps_flag = True
# ! transform result to v first?
# model_output =
model_output = get_mixed_prediction(True, model_output,
model.mixing_logit,
mixing_component)
if self.model_var_type in [
ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE
]:
assert model_output.shape == (B, C * 2, *x.shape[2:])
model_output, model_var_values = th.split(model_output, C, dim=1)
if self.model_var_type == ModelVarType.LEARNED:
model_log_variance = model_var_values
model_variance = th.exp(model_log_variance)
else:
min_log = _extract_into_tensor(
self.posterior_log_variance_clipped, t, x.shape)
max_log = _extract_into_tensor(np.log(self.betas), t, x.shape)
# The model_var_values is [-1, 1] for [min_var, max_var].
frac = (model_var_values + 1) / 2
model_log_variance = frac * max_log + (1 - frac) * min_log
model_variance = th.exp(model_log_variance)
else:
model_variance, model_log_variance = {
# for fixedlarge, we set the initial (log-)variance like so
# to get a better decoder log likelihood.
# ?
ModelVarType.FIXED_LARGE: ( # * used here
np.append(self.posterior_variance[1], self.betas[1:]),
np.log(
np.append(self.posterior_variance[1], self.betas[1:])),
),
ModelVarType.FIXED_SMALL: (
self.posterior_variance,
self.posterior_log_variance_clipped,
),
}[self.model_var_type]
model_variance = _extract_into_tensor(model_variance, t, x.shape)
model_log_variance = _extract_into_tensor(model_log_variance, t,
x.shape)
def process_xstart(x):
if denoised_fn is not None:
x = denoised_fn(x)
if clip_denoised:
return x.clamp(-1, 1)
return x
if self.model_mean_type == ModelMeanType.PREVIOUS_X:
pred_xstart = process_xstart(
self._predict_xstart_from_xprev(x_t=x, t=t,
xprev=model_output))
model_mean = model_output
elif self.model_mean_type in [
ModelMeanType.START_X, ModelMeanType.EPSILON, ModelMeanType.V
]:
if self.model_mean_type == ModelMeanType.START_X:
pred_xstart = process_xstart(model_output)
else: # * used here
if self.model_mean_type == ModelMeanType.V:
assert v_transformed_to_eps_flag # type: ignore
pred_xstart = process_xstart( # * return the x_0 using self._predict_xstart_from_eps as the denoised_fn
self._predict_xstart_from_eps(x_t=x, t=t,
eps=model_output))
model_mean, _, _ = self.q_posterior_mean_variance(
x_start=pred_xstart, x_t=x, t=t)
else:
raise NotImplementedError(self.model_mean_type)
assert (model_mean.shape == model_log_variance.shape ==
pred_xstart.shape == x.shape)
return {
"mean": model_mean,
"variance": model_variance,
"log_variance": model_log_variance,
"pred_xstart": pred_xstart,
}
def _predict_xstart_from_eps(self, x_t, t, eps):
assert x_t.shape == eps.shape
return (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t,
x_t.shape) * x_t -
_extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t,
x_t.shape) * eps)
def _predict_xstart_from_xprev(self, x_t, t, xprev):
assert x_t.shape == xprev.shape
return ( # (xprev - coef2*x_t) / coef1
_extract_into_tensor(1.0 / self.posterior_mean_coef1, t, x_t.shape)
* xprev - _extract_into_tensor(
self.posterior_mean_coef2 / self.posterior_mean_coef1, t,
x_t.shape) * x_t)
def _predict_eps_from_xstart(self, x_t, t, pred_xstart):
return (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t,
x_t.shape) * x_t -
pred_xstart) / _extract_into_tensor(
self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
# https://github.com/Stability-AI/stablediffusion/blob/cf1d67a6fd5ea1aa600c4df58e5b47da45f6bdbf/ldm/models/diffusion/ddpm.py#L288
def _predict_start_from_z_and_v(self, x_t, t, v):
# self.register_buffer('sqrt_alphas_cumprod', to_torch(np.sqrt(alphas_cumprod)))
# self.register_buffer('sqrt_one_minus_alphas_cumprod', to_torch(np.sqrt(1. - alphas_cumprod)))
return (_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_t.shape) *
x_t - _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod,
t, x_t.shape) * v)
def _predict_eps_from_z_and_v(self, x_t, t, v):
return (
_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_t.shape) * v +
_extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t,
x_t.shape) * x_t)
def _scale_timesteps(self, t):
if self.rescale_timesteps:
return t.float() * (1000.0 / self.num_timesteps)
return t
def condition_mean(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
"""
Compute the mean for the previous step, given a function cond_fn that
computes the gradient of a conditional log probability with respect to
x. In particular, cond_fn computes grad(log(p(y|x))), and we want to
condition on y.
This uses the conditioning strategy from Sohl-Dickstein et al. (2015).
"""
gradient = cond_fn(x, self._scale_timesteps(t), **model_kwargs)
new_mean = (p_mean_var["mean"].float() +
p_mean_var["variance"] * gradient.float())
return new_mean
def condition_score(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
"""
Compute what the p_mean_variance output would have been, should the
model's score function be conditioned by cond_fn.
See condition_mean() for details on cond_fn.
Unlike condition_mean(), this instead uses the conditioning strategy
from Song et al (2020).
"""
alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
eps = self._predict_eps_from_xstart(x, t, p_mean_var["pred_xstart"])
eps = eps - (1 - alpha_bar).sqrt() * cond_fn(
x, self._scale_timesteps(t), **model_kwargs)
out = p_mean_var.copy()
out["pred_xstart"] = self._predict_xstart_from_eps(x, t, eps)
out["mean"], _, _ = self.q_posterior_mean_variance(
x_start=out["pred_xstart"], x_t=x, t=t)
return out
def p_sample(
self,
model,
x,
t,
cond=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
mixing_normal=False,
):
"""
Sample x_{t-1} from the model at the given timestep.
:param model: the model to sample from.
:param x: the current tensor at x_{t-1}.
:param t: the value of t, starting at 0 for the first diffusion step.
:param clip_denoised: if True, clip the x_start prediction to [-1, 1].
:param denoised_fn: if not None, a function which applies to the
x_start prediction before it is used to sample.
:param cond_fn: if not None, this is a gradient function that acts
similarly to the model.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:return: a dict containing the following keys:
- 'sample': a random sample from the model.
- 'pred_xstart': a prediction of x_0.
"""
out = self.p_mean_variance(model,
x,
t,
c=cond,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
mixing_normal=mixing_normal)
noise = th.randn_like(x)
nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
) # no noise when t == 0
if cond_fn is not None:
out["mean"] = self.condition_mean(cond_fn,
out,
x,
t,
model_kwargs=model_kwargs)
sample = out["mean"] + nonzero_mask * th.exp(
0.5 * out["log_variance"]) * noise
return {"sample": sample, "pred_xstart": out["pred_xstart"]}
def get_mixing_component(self, x_noisy, t, enabled):
# alpha_bars = th.gather(self._alpha_bars, 0, timestep-1)
if enabled:
# one_minus_alpha_bars_sqrt = utils.view4D(th.sqrt(1.0 - alpha_bars), size)
one_minus_alpha_bars_sqrt = _extract_into_tensor(
self.sqrt_one_minus_alphas_cumprod, t, x_noisy.shape)
mixing_component = one_minus_alpha_bars_sqrt * x_noisy
else:
mixing_component = None
return mixing_component
def get_mixing_component_x0(self, x_noisy, t, enabled):
# alpha_bars = th.gather(self._alpha_bars, 0, timestep-1)
if enabled:
# one_minus_alpha_bars_sqrt = utils.view4D(th.sqrt(1.0 - alpha_bars), size)
one_minus_alpha_bars_sqrt = _extract_into_tensor(
self.sqrt_alphas_cumprod, t, x_noisy.shape)
mixing_component = one_minus_alpha_bars_sqrt * x_noisy
else:
mixing_component = None
return mixing_component
def p_sample_mixing_component(
self,
model,
x,
t,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
):
"""
Sample x_{t-1} from the model at the given timestep.
:param model: the model to sample from.
:param x: the current tensor at x_{t-1}.
:param t: the value of t, starting at 0 for the first diffusion step.
:param clip_denoised: if True, clip the x_start prediction to [-1, 1].
:param denoised_fn: if not None, a function which applies to the
x_start prediction before it is used to sample.
:param cond_fn: if not None, this is a gradient function that acts
similarly to the model.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:return: a dict containing the following keys:
- 'sample': a random sample from the model.
- 'pred_xstart': a prediction of x_0.
"""
assert self.model_mean_type == ModelMeanType.EPSILON, 'currently LSGM only implemented for EPSILON prediction'
out = self.p_mean_variance(
model,
x,
t / self.
num_timesteps, # trained on SDE diffusion, normalize steps to (0,1]
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
)
# mixing_component = self.get_mixing_component(x, t, enabled=True)
# out['mean'] = get_mixed_prediction(model.mixed_prediction, out['mean'], model.mixing_logit, mixing_component)
noise = th.randn_like(x)
nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
) # no noise when t == 0
if cond_fn is not None:
out["mean"] = self.condition_mean(cond_fn,
out,
x,
t,
model_kwargs=model_kwargs)
sample = out["mean"] + nonzero_mask * th.exp(
0.5 * out["log_variance"]) * noise
return {"sample": sample, "pred_xstart": out["pred_xstart"]}
def p_sample_loop(
self,
model,
shape,
cond=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
mixing_normal=False,
):
"""
Generate samples from the model.
:param model: the model module.
:param shape: the shape of the samples, (N, C, H, W).
:param noise: if specified, the noise from the encoder to sample.
Should be of the same shape as `shape`.
:param clip_denoised: if True, clip x_start predictions to [-1, 1].
:param denoised_fn: if not None, a function which applies to the
x_start prediction before it is used to sample.
:param cond_fn: if not None, this is a gradient function that acts
similarly to the model.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:param device: if specified, the device to create the samples on.
If not specified, use a model parameter's device.
:param progress: if True, show a tqdm progress bar.
:return: a non-differentiable batch of samples.
"""
final = None
for sample in self.p_sample_loop_progressive(
model,
shape,
cond=cond,
noise=noise,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
device=device,
progress=progress,
mixing_normal=mixing_normal):
final = sample
return final["sample"]
def p_sample_loop_progressive(
self,
model,
shape,
cond=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
mixing_normal=False,
):
"""
Generate samples from the model and yield intermediate samples from
each timestep of diffusion.
Arguments are the same as p_sample_loop().
Returns a generator over dicts, where each dict is the return value of
p_sample().
"""
if device is None:
device = dist_util.dev()
# device = next(model.parameters()).device
assert isinstance(shape, (tuple, list))
if noise is not None:
img = noise
else:
img = th.randn(*shape, device=device)
indices = list(range(self.num_timesteps))[::-1]
if progress:
# Lazy import so that we don't depend on tqdm.
from tqdm.auto import tqdm
indices = tqdm(indices)
for i in indices:
t = th.tensor([i] * shape[0], device=device)
with th.no_grad():
out = self.p_sample(model,
img,
t,
cond=cond,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
mixing_normal=mixing_normal)
yield out
img = out["sample"]
def ddim_sample(
self,
model,
x,
t,
cond=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
eta=0.0,
unconditional_guidance_scale=1.,
unconditional_conditioning=None,
mixing_normal=False,
objv_inference=False,
):
"""
Sample x_{t-1} from the model using DDIM.
Same usage as p_sample().
"""
if unconditional_guidance_scale != 1.0:
assert cond is not None
if unconditional_conditioning is None:
unconditional_conditioning = th.zeros_like(
cond['c_crossattn']
) # ImageEmbedding adopts zero as the null embedding
if unconditional_conditioning is None or unconditional_guidance_scale == 1.:
# e_t = self.model.apply_model(x, t, c)
out = self.p_mean_variance(
model,
x,
t,
c=cond,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
mixing_normal=mixing_normal,
)
eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
elif objv_inference:
assert cond is not None
x_in = th.cat([x] * 2)
t_in = th.cat([t] * 2)
c_in = {}
for k in cond:
c_in[k] = th.cat([
unconditional_conditioning[k].repeat_interleave(
cond[k].shape[0], 0), cond[k]
])
model_uncond, model_t = self.p_mean_variance(
model,
x_in,
t_in,
c=c_in,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
mixing_normal=mixing_normal,
direct_return_model_output=True, # ! compat with _wrapper
).chunk(2)
# Usually our model outputs epsilon, but we re-derive it
# model_uncond, model_t = model(x_in, self._scale_timesteps(t_in), c=c_in, mixing_normal=mixing_normal, **model_kwargs).chunk(2)
# in case we used x_start or x_prev prediction.
# st()
# ! guidance
# e_t_uncond, e_t = eps.chunk(2)
model_out = model_uncond + unconditional_guidance_scale * (
model_t - model_uncond)
if self.model_mean_type == ModelMeanType.V:
eps = self._predict_eps_from_z_and_v(x, t, model_out)
# eps = self._predict_eps_from_xstart(x_in, t_in, out["pred_xstart"])
else:
assert cond is not None
x_in = th.cat([x] * 2)
t_in = th.cat([t] * 2)
c_in = {
'c_crossattn':
th.cat([
unconditional_conditioning.repeat_interleave(
cond['c_crossattn'].shape[0], dim=0),
cond['c_crossattn']
])
}
# c_in = {}
# for k in cond:
# c_in[k] = th.cat([unconditional_conditioning[k], cond[k]])
out = self.p_mean_variance(
model,
x_in,
t_in,
c=c_in,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
mixing_normal=mixing_normal,
)
# Usually our model outputs epsilon, but we re-derive it
# in case we used x_start or x_prev prediction.
eps = self._predict_eps_from_xstart(x_in, t_in, out["pred_xstart"])
# ! guidance
e_t_uncond, e_t = eps.chunk(2)
# st()
eps = e_t_uncond + unconditional_guidance_scale * (e_t -
e_t_uncond)
if cond_fn is not None:
out = self.condition_score(cond_fn,
out,
x,
t,
model_kwargs=model_kwargs)
# eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
# ! re-derive xstart
pred_x0 = self._predict_xstart_from_eps(x, t, eps)
alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t,
x.shape)
sigma = (eta * th.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar)) *
th.sqrt(1 - alpha_bar / alpha_bar_prev))
# Equation 12.
noise = th.randn_like(x)
mean_pred = (pred_x0 * th.sqrt(alpha_bar_prev) +
th.sqrt(1 - alpha_bar_prev - sigma**2) * eps)
nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
) # no noise when t == 0
sample = mean_pred + nonzero_mask * sigma * noise
return {"sample": sample, "pred_xstart": pred_x0}
def ddim_reverse_sample(
self,
model,
x,
t,
clip_denoised=True,
denoised_fn=None,
model_kwargs=None,
eta=0.0,
):
"""
Sample x_{t+1} from the model using DDIM reverse ODE.
"""
assert eta == 0.0, "Reverse ODE only for deterministic path"
out = self.p_mean_variance(
model,
x,
t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
)
# Usually our model outputs epsilon, but we re-derive it
# in case we used x_start or x_prev prediction.
eps = (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x.shape)
* x - out["pred_xstart"]) / _extract_into_tensor(
self.sqrt_recipm1_alphas_cumprod, t, x.shape)
alpha_bar_next = _extract_into_tensor(self.alphas_cumprod_next, t,
x.shape)
# Equation 12. reversed
mean_pred = (out["pred_xstart"] * th.sqrt(alpha_bar_next) +
th.sqrt(1 - alpha_bar_next) * eps)
return {"sample": mean_pred, "pred_xstart": out["pred_xstart"]}
def ddim_sample_loop(
self,
model,
shape,
cond=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
eta=0.0,
mixing_normal=False,
unconditional_guidance_scale=1.0,
unconditional_conditioning=None,
objv_inference=False,
):
"""
Generate samples from the model using DDIM.
Same usage as p_sample_loop().
"""
final = None
for sample in self.ddim_sample_loop_progressive(
model,
shape,
cond=cond,
noise=noise,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
device=device,
progress=progress,
eta=eta,
mixing_normal=mixing_normal,
unconditional_guidance_scale=unconditional_guidance_scale,
unconditional_conditioning=unconditional_conditioning,
objv_inference=objv_inference,
):
final = sample
return final["sample"]
def ddim_sample_loop_progressive(
self,
model,
shape,
cond=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
eta=0.0,
mixing_normal=False,
unconditional_guidance_scale=1.0,
unconditional_conditioning=None,
objv_inference=False,
):
"""
Use DDIM to sample from the model and yield intermediate samples from
each timestep of DDIM.
Same usage as p_sample_loop_progressive().
"""
if device is None:
device = next(model.parameters()).device
assert isinstance(shape, (tuple, list))
if noise is not None:
img = noise
else:
img = th.randn(*shape, device=device)
indices = list(range(self.num_timesteps))[::-1]
if progress:
# Lazy import so that we don't depend on tqdm.
from tqdm.auto import tqdm
indices = tqdm(indices)
for i in indices:
t = th.tensor([i] * shape[0], device=device)
with th.no_grad():
out = self.ddim_sample(
model,
img,
t,
cond=cond,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
eta=eta,
mixing_normal=mixing_normal,
unconditional_guidance_scale=unconditional_guidance_scale,
unconditional_conditioning=unconditional_conditioning,
objv_inference=objv_inference,
)
yield out
img = out["sample"]
def _vb_terms_bpd(self,
model,
x_start,
x_t,
t,
clip_denoised=True,
model_kwargs=None):
"""
Get a term for the variational lower-bound.
The resulting units are bits (rather than nats, as one might expect).
This allows for comparison to other papers.
:return: a dict with the following keys:
- 'output': a shape [N] tensor of NLLs or KLs.
- 'pred_xstart': the x_0 predictions.
"""
true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance(
x_start=x_start, x_t=x_t, t=t)
out = self.p_mean_variance(model,
x_t,
t,
clip_denoised=clip_denoised,
model_kwargs=model_kwargs)
kl = normal_kl(true_mean, true_log_variance_clipped, out["mean"],
out["log_variance"])
kl = mean_flat(kl) / np.log(2.0)
decoder_nll = -discretized_gaussian_log_likelihood(
x_start, means=out["mean"], log_scales=0.5 * out["log_variance"])
assert decoder_nll.shape == x_start.shape
decoder_nll = mean_flat(decoder_nll) / np.log(2.0)
# At the first timestep return the decoder NLL,
# otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t))
output = th.where((t == 0), decoder_nll, kl)
return {"output": output, "pred_xstart": out["pred_xstart"]}
def training_losses(self,
model,
x_start,
t,
model_kwargs=None,
noise=None,
return_detail=False):
"""
Compute training losses for a single timestep.
:param model: the model to evaluate loss on.
:param x_start: the [N x C x ...] tensor of inputs.
:param t: a batch of timestep indices.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:param noise: if specified, the specific Gaussian noise to try to remove.
:return: a dict with the key "loss" containing a tensor of shape [N].
Some mean or variance settings may also have other keys.
"""
if model_kwargs is None: # * micro_cond
model_kwargs = {}
if noise is None:
noise = th.randn_like(x_start) # x_start is the x0 image
x_t = self.q_sample(x_start,
t,
noise=noise,
return_detail=return_detail
) # * add noise according to predefined schedule
if return_detail:
x_t, alpha_bar, _ = x_t
# terms = {}
terms = {"x_t": x_t}
if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL:
terms["loss"] = self._vb_terms_bpd(
model=model,
x_start=x_start,
x_t=x_t,
t=t,
clip_denoised=False,
model_kwargs=model_kwargs,
)["output"]
if self.loss_type == LossType.RESCALED_KL:
terms["loss"] *= self.num_timesteps
elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE:
model_output = model(
x_t, self._scale_timesteps(t), **model_kwargs
) # directly predict epsilon or x_0; no learned sigma
if self.model_var_type in [
ModelVarType.LEARNED,
ModelVarType.LEARNED_RANGE,
]:
B, C = x_t.shape[:2]
assert model_output.shape == (B, C * 2, *x_t.shape[2:])
model_output, model_var_values = th.split(model_output,
C,
dim=1)
# Learn the variance using the variational bound, but don't let
# it affect our mean prediction.
frozen_out = th.cat([model_output.detach(), model_var_values],
dim=1)
terms["vb"] = self._vb_terms_bpd(
model=lambda *args, r=frozen_out: r,
x_start=x_start,
x_t=x_t,
t=t,
clip_denoised=False,
)["output"]
if self.loss_type == LossType.RESCALED_MSE:
# Divide by 1000 for equivalence with initial implementation.
# Without a factor of 1/1000, the VB term hurts the MSE term.
terms["vb"] *= self.num_timesteps / 1000.0
target = {
ModelMeanType.PREVIOUS_X:
self.q_posterior_mean_variance(x_start=x_start, x_t=x_t,
t=t)[0],
ModelMeanType.START_X:
x_start,
ModelMeanType.EPSILON:
noise,
}[self.model_mean_type] # ModelMeanType.EPSILON
# st()
assert model_output.shape == target.shape == x_start.shape
terms["mse"] = mean_flat((target - model_output)**2)
terms['model_output'] = model_output
# terms['target'] = target # TODO, flag.
if return_detail:
terms.update({
'diffusion_target': target,
'alpha_bar': alpha_bar,
# 'one_minus_alpha':one_minus_alpha
# 'noise': noise
})
if "vb" in terms:
terms["loss"] = terms["mse"] + terms["vb"]
else:
terms["loss"] = terms["mse"]
else:
raise NotImplementedError(self.loss_type)
return terms
def _prior_bpd(self, x_start):
"""
Get the prior KL term for the variational lower-bound, measured in
bits-per-dim.
This term can't be optimized, as it only depends on the encoder.
:param x_start: the [N x C x ...] tensor of inputs.
:return: a batch of [N] KL values (in bits), one per batch element.
"""
batch_size = x_start.shape[0]
t = th.tensor([self.num_timesteps - 1] * batch_size,
device=x_start.device)
qt_mean, _, qt_log_variance = self.q_mean_variance(x_start, t)
kl_prior = normal_kl(mean1=qt_mean,
logvar1=qt_log_variance,
mean2=0.0,
logvar2=0.0)
return mean_flat(kl_prior) / np.log(2.0)
def calc_bpd_loop(self,
model,
x_start,
clip_denoised=True,
model_kwargs=None):
"""
Compute the entire variational lower-bound, measured in bits-per-dim,
as well as other related quantities.
:param model: the model to evaluate loss on.
:param x_start: the [N x C x ...] tensor of inputs.
:param clip_denoised: if True, clip denoised samples.
:param model_kwargs: if not None, a dict of extra keyword arguments to
pass to the model. This can be used for conditioning.
:return: a dict containing the following keys:
- total_bpd: the total variational lower-bound, per batch element.
- prior_bpd: the prior term in the lower-bound.
- vb: an [N x T] tensor of terms in the lower-bound.
- xstart_mse: an [N x T] tensor of x_0 MSEs for each timestep.
- mse: an [N x T] tensor of epsilon MSEs for each timestep.
"""
device = x_start.device
batch_size = x_start.shape[0]
vb = []
xstart_mse = []
mse = []
for t in list(range(self.num_timesteps))[::-1]:
t_batch = th.tensor([t] * batch_size, device=device)
noise = th.randn_like(x_start)
x_t = self.q_sample(x_start=x_start, t=t_batch, noise=noise)
# Calculate VLB term at the current timestep
with th.no_grad():
out = self._vb_terms_bpd(
model,
x_start=x_start,
x_t=x_t,
t=t_batch,
clip_denoised=clip_denoised,
model_kwargs=model_kwargs,
)
vb.append(out["output"])
xstart_mse.append(mean_flat((out["pred_xstart"] - x_start)**2))
eps = self._predict_eps_from_xstart(x_t, t_batch,
out["pred_xstart"])
mse.append(mean_flat((eps - noise)**2))
vb = th.stack(vb, dim=1)
xstart_mse = th.stack(xstart_mse, dim=1)
mse = th.stack(mse, dim=1)
prior_bpd = self._prior_bpd(x_start)
total_bpd = vb.sum(dim=1) + prior_bpd
return {
"total_bpd": total_bpd,
"prior_bpd": prior_bpd,
"vb": vb,
"xstart_mse": xstart_mse,
"mse": mse,
}
def _extract_into_tensor(arr, timesteps, broadcast_shape):
"""
Extract values from a 1-D numpy array for a batch of indices.
:param arr: the 1-D numpy array.
:param timesteps: a tensor of indices into the array to extract.
:param broadcast_shape: a larger shape of K dimensions with the batch
dimension equal to the length of timesteps.
:return: a tensor of shape [batch_size, 1, ...] where the shape has K dims.
"""
res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float()
while len(res.shape) < len(broadcast_shape):
res = res[..., None]
return res.expand(broadcast_shape)
|