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"""
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
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)
else:
# st()
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
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,
):
"""
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 = {
k: th.zeros_like(cond[k]) for k in cond.keys()
}
# ImageEmbedding adopts zero as the null embedding
# st()
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"])
else:
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], 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"])
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,
):
"""
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,
):
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,
):
"""
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,
)
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)
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