"""
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 .DiffAE_model_unet_autoenc import AutoencReturn
from .DiffAE_support_config_base import BaseConfig
import enum
import math
import numpy as np
import torch as th
from .DiffAE_model import *
from .DiffAE_model_nn import mean_flat
from typing import NamedTuple, Tuple
from .DiffAE_support_choices import *
from torch.cuda.amp import autocast
import torch.nn.functional as F
from dataclasses import dataclass
@dataclass
class GaussianDiffusionBeatGansConfig(BaseConfig):
gen_type: GenerativeType
betas: Tuple[float]
model_type: ModelType
model_mean_type: ModelMeanType
model_var_type: ModelVarType
loss_type: LossType
rescale_timesteps: bool
fp16: bool
train_pred_xstart_detach: bool = True
def make_sampler(self):
return GaussianDiffusionBeatGans(self)
class GaussianDiffusionBeatGans:
"""
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).
"""
def __init__(self, conf: GaussianDiffusionBeatGansConfig):
self.conf = conf
self.model_mean_type = conf.model_mean_type
self.model_var_type = conf.model_var_type
self.loss_type = conf.loss_type
self.rescale_timesteps = conf.rescale_timesteps
# Use float64 for accuracy.
betas = np.array(conf.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)
# 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 training_losses(self,
model: Model,
x_start: th.Tensor,
t: th.Tensor,
model_kwargs=None,
noise: th.Tensor = None):
"""
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:
model_kwargs = {}
if noise is None:
noise = th.randn_like(x_start)
x_t = self.q_sample(x_start, t, noise=noise)
terms = {'x_t': x_t}
if self.loss_type in [
LossType.mse,
LossType.l1,
]:
with autocast(self.conf.fp16):
# x_t is static wrt. to the diffusion process
model_forward = model.forward(x=x_t.detach(),
t=self._scale_timesteps(t),
x_start=x_start.detach(),
**model_kwargs)
model_output = model_forward.pred
_model_output = model_output
if self.conf.train_pred_xstart_detach:
_model_output = _model_output.detach()
# get the pred xstart
p_mean_var = self.p_mean_variance(
model=DummyModel(pred=_model_output),
# gradient goes through x_t
x=x_t,
t=t,
clip_denoised=False)
terms['pred_xstart'] = p_mean_var['pred_xstart']
# model_output = model(x_t, self._scale_timesteps(t), **model_kwargs)
target_types = {
ModelMeanType.eps: noise,
}
target = target_types[self.model_mean_type]
assert model_output.shape == target.shape == x_start.shape
if self.loss_type == LossType.mse:
if self.model_mean_type == ModelMeanType.eps:
# (n, c, h, w) => (n, )
terms["mse"] = mean_flat((target - model_output)**2)
else:
raise NotImplementedError()
elif self.loss_type == LossType.l1:
# (n, c, h, w) => (n, )
terms["mse"] = mean_flat((target - model_output).abs())
else:
raise NotImplementedError()
if "vb" in terms:
# if learning the variance also use the vlb loss
terms["loss"] = terms["mse"] + terms["vb"]
else:
terms["loss"] = terms["mse"]
else:
raise NotImplementedError(self.loss_type)
return terms
def sample(self,
model: Model,
shape=None,
noise=None,
cond=None,
x_start=None,
clip_denoised=True,
model_kwargs=None,
progress=False):
"""
Args:
x_start: given for the autoencoder
"""
if model_kwargs is None:
model_kwargs = {}
if self.conf.model_type.has_autoenc():
model_kwargs['x_start'] = x_start
model_kwargs['cond'] = cond
if self.conf.gen_type == GenerativeType.ddpm:
return self.p_sample_loop(model,
shape=shape,
noise=noise,
clip_denoised=clip_denoised,
model_kwargs=model_kwargs,
progress=progress)
elif self.conf.gen_type == GenerativeType.ddim:
return self.ddim_sample_loop(model,
shape=shape,
noise=noise,
clip_denoised=clip_denoised,
model_kwargs=model_kwargs,
progress=progress)
else:
raise NotImplementedError()
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):
"""
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
return (
_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) *
x_start + _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod,
t, x_start.shape) * noise)
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: Model,
x,
t,
clip_denoised=True,
denoised_fn=None,
model_kwargs=None):
"""
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.
"""
if model_kwargs is None:
model_kwargs = {}
B, C = x.shape[:2]
assert t.shape == (B, )
with autocast(self.conf.fp16):
model_forward = model.forward(x=x,
t=self._scale_timesteps(t),
**model_kwargs)
model_output = model_forward.pred
if self.model_var_type in [
ModelVarType.fixed_large, ModelVarType.fixed_small
]:
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: (
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 in [
ModelMeanType.eps,
]:
if self.model_mean_type == ModelMeanType.eps:
pred_xstart = process_xstart(
self._predict_xstart_from_eps(x_t=x, t=t,
eps=model_output))
else:
raise NotImplementedError()
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,
'model_forward': model_forward,
}
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_xstart_from_scaled_xstart(self, t, scaled_xstart):
return scaled_xstart * _extract_into_tensor(
self.sqrt_recip_alphas_cumprod, t, scaled_xstart.shape)
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)
def _predict_eps_from_scaled_xstart(self, x_t, t, scaled_xstart):
"""
Args:
scaled_xstart: is supposed to be sqrt(alphacum) * x_0
"""
# 1 / sqrt(1-alphabar) * (x_t - scaled xstart)
return (x_t - scaled_xstart) / _extract_into_tensor(
self.sqrt_one_minus_alphas_cumprod, t, x_t.shape)
def _scale_timesteps(self, t):
if self.rescale_timesteps:
# scale t to be maxed out at 1000 steps
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: 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.
"""
out = self.p_mean_variance(
model,
x,
t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
)
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: Model,
shape=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=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,
noise=noise,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
device=device,
progress=progress,
):
final = sample
return final["sample"]
def p_sample_loop_progressive(
self,
model: Model,
shape=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=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 = next(model.parameters()).device
if noise is not None:
img = noise
else:
assert isinstance(shape, (tuple, list))
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)
t = th.tensor([i] * len(img), device=device)
with th.no_grad():
out = self.p_sample(
model,
img,
t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
)
yield out
img = out["sample"]
def ddim_sample(
self,
model: Model,
x,
t,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
eta=0.0,
):
"""
Sample x_{t-1} from the model using DDIM.
Same usage as p_sample().
"""
out = self.p_mean_variance(
model,
x,
t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
)
if cond_fn is not None:
out = self.condition_score(cond_fn,
out,
x,
t,
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 = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
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 = (out["pred_xstart"] * 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": out["pred_xstart"]}
def ddim_reverse_sample(
self,
model: 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.
NOTE: never used ?
"""
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 (DDIM paper) (th.sqrt == torch.sqrt)
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_reverse_sample_loop(
self,
model: Model,
x,
clip_denoised=True,
denoised_fn=None,
model_kwargs=None,
eta=0.0,
device=None,
):
if device is None:
device = next(model.parameters()).device
sample_t = []
xstart_t = []
T = []
indices = list(range(self.num_timesteps))
sample = x
for i in indices:
t = th.tensor([i] * len(sample), device=device)
with th.no_grad():
out = self.ddim_reverse_sample(model,
sample,
t=t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
model_kwargs=model_kwargs,
eta=eta)
sample = out['sample']
# [1, ..., T]
sample_t.append(sample)
# [0, ...., T-1]
xstart_t.append(out['pred_xstart'])
# [0, ..., T-1] ready to use
T.append(t)
return {
# xT "
'sample': sample,
# (1, ..., T)
'sample_t': sample_t,
# xstart here is a bit different from sampling from T = T-1 to T = 0
# may not be exact
'xstart_t': xstart_t,
'T': T,
}
def ddim_sample_loop(
self,
model: Model,
shape=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
eta=0.0,
):
"""
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,
noise=noise,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=model_kwargs,
device=device,
progress=progress,
eta=eta,
):
final = sample
return final["sample"]
def ddim_sample_loop_progressive(
self,
model: Model,
shape=None,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=False,
eta=0.0,
):
"""
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
if noise is not None:
img = noise
else:
assert isinstance(shape, (tuple, list))
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:
if isinstance(model_kwargs, list):
# index dependent model kwargs
# (T-1, ..., 0)
_kwargs = model_kwargs[i]
else:
_kwargs = model_kwargs
t = th.tensor([i] * len(img), device=device)
with th.no_grad():
out = self.ddim_sample(
model,
img,
t,
clip_denoised=clip_denoised,
denoised_fn=denoised_fn,
cond_fn=cond_fn,
model_kwargs=_kwargs,
eta=eta,
)
out['t'] = t
yield out
img = out["sample"]
def _vb_terms_bpd(self,
model: 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"],
'model_forward': out['model_forward'],
}
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: 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)
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":
# 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 == "cosine":
return betas_for_alpha_bar(
num_diffusion_timesteps,
lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2)**2,
)
elif schedule_name == "const0.01":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.01] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.015":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.015] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.008":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.008] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0065":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0065] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0055":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0055] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0045":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0045] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0035":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0035] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0025":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0025] * num_diffusion_timesteps,
dtype=np.float64)
elif schedule_name == "const0.0015":
scale = 1000 / num_diffusion_timesteps
return np.array([scale * 0.0015] * num_diffusion_timesteps,
dtype=np.float64)
else:
raise NotImplementedError(f"unknown beta schedule: {schedule_name}")
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)
def normal_kl(mean1, logvar1, mean2, logvar2):
"""
Compute the KL divergence between two gaussians.
Shapes are automatically broadcasted, so batches can be compared to
scalars, among other use cases.
"""
tensor = None
for obj in (mean1, logvar1, mean2, logvar2):
if isinstance(obj, th.Tensor):
tensor = obj
break
assert tensor is not None, "at least one argument must be a Tensor"
# Force variances to be Tensors. Broadcasting helps convert scalars to
# Tensors, but it does not work for th.exp().
logvar1, logvar2 = [
x if isinstance(x, th.Tensor) else th.tensor(x).to(tensor)
for x in (logvar1, logvar2)
]
return 0.5 * (-1.0 + logvar2 - logvar1 + th.exp(logvar1 - logvar2) +
((mean1 - mean2)**2) * th.exp(-logvar2))
def approx_standard_normal_cdf(x):
"""
A fast approximation of the cumulative distribution function of the
standard normal.
"""
return 0.5 * (
1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3))))
def discretized_gaussian_log_likelihood(x, *, means, log_scales):
"""
Compute the log-likelihood of a Gaussian distribution discretizing to a
given image.
:param x: the target images. It is assumed that this was uint8 values,
rescaled to the range [-1, 1].
:param means: the Gaussian mean Tensor.
:param log_scales: the Gaussian log stddev Tensor.
:return: a tensor like x of log probabilities (in nats).
"""
assert x.shape == means.shape == log_scales.shape
centered_x = x - means
inv_stdv = th.exp(-log_scales)
plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
cdf_plus = approx_standard_normal_cdf(plus_in)
min_in = inv_stdv * (centered_x - 1.0 / 255.0)
cdf_min = approx_standard_normal_cdf(min_in)
log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
cdf_delta = cdf_plus - cdf_min
log_probs = th.where(
x < -0.999,
log_cdf_plus,
th.where(x > 0.999, log_one_minus_cdf_min,
th.log(cdf_delta.clamp(min=1e-12))),
)
assert log_probs.shape == x.shape
return log_probs
class DummyModel(th.nn.Module):
def __init__(self, pred):
super().__init__()
self.pred = pred
def forward(self, *args, **kwargs):
return DummyReturn(pred=self.pred)
class DummyReturn(NamedTuple):
pred: th.Tensor