DL-Art-School/codes/models/diffusion/gaussian_diffusion.py
2022-07-17 18:24:43 -06:00

1196 lines
46 KiB
Python

"""
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.
"""
import enum
import math
import random
import numpy as np
import torch
import torch as th
from tqdm import tqdm
from models.diffusion.nn import mean_flat
from models.diffusion.losses import normal_kl, discretized_gaussian_log_likelihood
def causal_timestep_adjustment(t, S, num_timesteps, causal_slope=1, add_jitter=True):
"""
Remaps [t] from a batch of integers into a causal sequence [S] long where each sequence element is [causal_slope]
timesteps advanced from the previous sequence element. At t=0, the sequence is all 0s and at t=[num_timesteps], the
sequence is all [num_timesteps].
As a result of the last property, longer sequences will have larger "gaps" between them in continuous space. This must
be considered at inference time. Specifically, you should allot ((num_timesteps+causal_slope*(seq_len-1))/num_timesteps)
times more timesteps in inference for the same quality.
:param t: Batched timestep integers
:param S: Sequence length.
:param num_timesteps: Number of total timesteps.
:param causal_slope: The causal slope. Ex: "2" means each sequence element will be 2 timesteps ahead of its predecessor.
:param add_jitter: Whether or not to add random jitter into the extra gaps between timesteps added by this function.
Should be true for training and false for inference.
:return: [b,S] sequence of timestep integers.
"""
S_sloped = causal_slope * (S-1)
# This algorithm for adding causality does so by simply adding S_sloped additional timesteps. To make this
# actually work, we map the existing t from the timescale specified to the model to the causal timescale:
adj_t = torch.div(t * (num_timesteps + S_sloped), num_timesteps, rounding_mode='floor')
adj_t = adj_t - S_sloped
if add_jitter:
t_gap = (num_timesteps + S_sloped) / num_timesteps
jitter = (2*random.random()-1) * t_gap
adj_t = (adj_t+jitter).clamp(-S_sloped, num_timesteps)
# Now use the re-mapped adj_t to create a timestep vector that propagates across the sequence with the specified slope.
t = adj_t.unsqueeze(1).repeat(1, S)
t = (t + torch.arange(0, S, device=t.device) * causal_slope).clamp(-1, num_timesteps).long()
return t
def causal_mask_and_fix(t, num_timesteps):
mask1 = t == num_timesteps
t[mask1] = num_timesteps-1
mask2 = t == -1
t[mask2] = 0
return t, mask1.logical_or(mask2)
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,
)
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)
class ModelMeanType(enum.Enum):
"""
Which type of output the model predicts.
"""
PREVIOUS_X = 'previous_x' # the model predicts x_{t-1}
START_X = 'start_x' # the model predicts x_0
EPSILON = 'epsilon' # the model predicts epsilon
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 = 'learned'
FIXED_SMALL = 'fixed_small'
FIXED_LARGE = 'fixed_large'
LEARNED_RANGE = 'learned_range'
class LossType(enum.Enum):
MSE = 'mse' # use raw MSE loss (and KL when learning variances)
RESCALED_MSE = 'rescaled_mse' # use raw MSE loss (with RESCALED_KL when learning variances)
KL = 'kl' # use the variational lower-bound
RESCALED_KL = 'rescaled_kl' # 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).
"""
def __init__(
self,
*,
betas,
model_mean_type,
model_var_type,
loss_type,
rescale_timesteps=False,
conditioning_free=False,
conditioning_free_k=1,
ramp_conditioning_free=True,
):
self.model_mean_type = ModelMeanType(model_mean_type)
self.model_var_type = ModelVarType(model_var_type)
self.loss_type = LossType(loss_type)
self.rescale_timesteps = rescale_timesteps
self.conditioning_free = conditioning_free
self.conditioning_free_k = conditioning_free_k
self.ramp_conditioning_free = ramp_conditioning_free
# 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)
# 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):
"""
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, 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,) or t.shape == (B,1,x.shape[-1])
model_output = model(x, self._scale_timesteps(t), **model_kwargs)
if self.conditioning_free:
model_output_no_conditioning = model(x, self._scale_timesteps(t), conditioning_free=True, **model_kwargs)
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.conditioning_free:
model_output_no_conditioning, _ = th.split(model_output_no_conditioning, 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: (
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)
if self.conditioning_free:
if self.ramp_conditioning_free:
assert t.shape[0] == 1 # This should only be used in inference.
cfk = self.conditioning_free_k * (1 - self._scale_timesteps(t).float().mean().item() / self.num_timesteps)
else:
cfk = self.conditioning_free_k
model_output = (1 + cfk) * model_output - cfk * model_output_no_conditioning
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]:
if self.model_mean_type == ModelMeanType.START_X:
pred_xstart = process_xstart(model_output)
else:
pred_xstart = process_xstart(
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)
def _scale_timesteps(self, t):
if self.rescale_timesteps:
return t.float() * (1000.0 / self.num_timesteps)
return t
def _get_scale_ratio(self):
return 1
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,
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)
if len(t.shape) == 1:
nonzero_mask = (
(t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
) # no noise when t == 0
else:
nonzero_mask = (t != 0).float()
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,
noise=None,
clip_denoised=True,
causal=False,
causal_slope=1,
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,
causal=causal,
causal_slope=causal_slope,
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,
shape,
noise=None,
clip_denoised=True,
causal=False,
causal_slope=1,
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
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]
orig_img = img
for i in tqdm(indices):
t = th.tensor([i] * shape[0], device=device)
mask = torch.zeros_like(img)
if causal:
t = causal_timestep_adjustment(t, shape[-1], self.num_timesteps, causal_slope * self._get_scale_ratio(), add_jitter=False).unsqueeze(1)
t, mask = causal_mask_and_fix(t, self.num_timesteps)
mask = mask.repeat(img.shape[0], img.shape[1], 1)
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"]
if torch.any(mask):
img[mask] = orig_img[mask] # For causal diffusion, keep resetting these predictions until they are unmasked.
orig_img = img
def p_sample_loop_with_guidance(
self,
model,
guidance_input,
mask,
noise=None,
clip_denoised=True,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
):
if device is None:
device = next(model.parameters()).device
shape = guidance_input.shape
if noise is None:
noise = th.randn(*shape, device=device)
indices = list(range(self.num_timesteps))[::-1]
img = noise
for i in tqdm(indices):
t = th.tensor([i] * shape[0], 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,
)
model_driven_out = out["sample"] * mask.logical_not()
guidance_driven_out = self.q_sample(guidance_input, t, noise=noise) * mask
img = model_driven_out + guidance_driven_out
return img
def ddim_sample(
self,
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
)
if len(t.shape) == 2:
nonzero_mask = (
(t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
) # no noise when t == 0
else:
nonzero_mask = (t != 0).float()
sample = mean_pred + nonzero_mask * sigma * noise
return {"sample": sample, "pred_xstart": out["pred_xstart"]}
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,
noise=None,
clip_denoised=True,
causal=False,
causal_slope=1,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=True,
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,
causal=causal,
causal_slope=causal_slope,
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_with_guidance(
self,
model,
guidance_input,
mask,
noise=None,
clip_denoised=True,
causal=False,
causal_slope=1,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
eta=0.0,
):
device = guidance_input.device
shape = guidance_input.shape
if noise is not None:
img = noise
else:
img = th.randn(*shape, device=device)
indices = list(range(self.num_timesteps))[::-1]
orig_img = img
for i in tqdm(indices):
t = th.tensor([i] * shape[0], device=device)
c_mask = torch.zeros_like(img)
if causal:
t = causal_timestep_adjustment(t, shape[-1], self.num_timesteps, causal_slope * self._get_scale_ratio(), add_jitter=False).unsqueeze(1)
t, c_mask = causal_mask_and_fix(t, self.num_timesteps)
t[c_mask] = self.num_timesteps-1
c_mask = c_mask.repeat(img.shape[0], img.shape[1], 1)
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=model_kwargs,
eta=eta,
)
model_driven_out = out["sample"] * mask.logical_not()
if torch.any(c_mask):
model_driven_out[c_mask] = orig_img[c_mask] # For causal diffusion, keep resetting these predictions until they are unmasked.
guidance_driven_out = self.q_sample(guidance_input, t, noise=noise) * mask
img = model_driven_out + guidance_driven_out
orig_img = orig_img
return img
def ddim_sample_loop_progressive(
self,
model,
shape,
noise=None,
clip_denoised=True,
causal=False,
causal_slope=1,
denoised_fn=None,
cond_fn=None,
model_kwargs=None,
device=None,
progress=True,
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
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)
orig_img = img
for i in indices:
t = th.tensor([i] * shape[0], device=device)
mask = torch.zeros_like(img)
if causal:
t = causal_timestep_adjustment(t, shape[-1], self.num_timesteps, causal_slope * self._get_scale_ratio(), add_jitter=False).unsqueeze(1)
t, mask = causal_mask_and_fix(t, self.num_timesteps)
t[mask] = self.num_timesteps-1
mask = mask.repeat(img.shape[0], img.shape[1], 1)
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=model_kwargs,
eta=eta,
)
yield out
img = out["sample"]
if torch.any(mask):
img[mask] = orig_img[mask] # For causal diffusion, keep resetting these predictions until they are unmasked.
orig_img = orig_img
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 = 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 = 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))
if len(t.shape) == 1:
output = th.where((t == 0).view(-1, 1, 1), decoder_nll, kl)
else:
output = th.where((t == 0), decoder_nll, kl)
return {"output": output, "pred_xstart": out["pred_xstart"]}
def causal_training_losses(self, model, x_start, t, causal_slope=1, model_kwargs=None, noise=None, channel_balancing_fn=None):
"""
Compute training losses for a causal diffusion process.
"""
assert len(x_start.shape) == 3, "causal_training_losses assumes a 1d sequence with the axis being the time axis."
ct = causal_timestep_adjustment(t, x_start.shape[-1], self.num_timesteps, causal_slope * self._get_scale_ratio(), add_jitter=True)
ct = ct.unsqueeze(1) # Necessary to make the output shape compatible with x_start.
return self.training_losses(model, x_start, ct, model_kwargs, noise, channel_balancing_fn)
def training_losses(self, model, x_start, t, model_kwargs=None, noise=None, channel_balancing_fn=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)
if len(t.shape) == 3:
t, t_mask = causal_mask_and_fix(t, self.num_timesteps)
t_mask = t_mask.logical_not() # This is used to mask out losses for timesteps that are out of bounds.
else:
t_mask = torch.ones_like(x_start)
x_t = self.q_sample(x_start, t, noise=noise)
terms = {}
if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL:
# TODO: support multiple model outputs for this mode.
terms["loss"] = mean_flat(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_outputs = model(x_t, self._scale_timesteps(t), **model_kwargs)
if isinstance(model_outputs, tuple):
model_output = model_outputs[0]
terms['extra_outputs'] = model_outputs[1:]
else:
model_output = model_outputs
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
if self.model_mean_type == ModelMeanType.PREVIOUS_X:
target = self.q_posterior_mean_variance(
x_start=x_start, x_t=x_t, t=t
)[0]
x_start_pred = torch.zeros(x_start) # Not supported.
elif self.model_mean_type == ModelMeanType.START_X:
target = x_start
x_start_pred = model_output
elif self.model_mean_type == ModelMeanType.EPSILON:
target = noise
x_start_pred = self._predict_xstart_from_eps(x_t, t, model_output)
else:
raise NotImplementedError(self.model_mean_type)
assert model_output.shape == target.shape == x_start.shape
s_err = t_mask * (target - model_output) ** 2
if channel_balancing_fn is not None:
s_err = channel_balancing_fn(s_err)
terms["mse_by_batch"] = s_err.reshape(s_err.shape[0], -1).mean(dim=1)
terms["mse"] = mean_flat(s_err)
terms["vb"] = terms["vb"] * t_mask
terms["x_start_predicted"] = x_start_pred
if "vb" in terms:
if channel_balancing_fn is not None:
terms["vb"] = channel_balancing_fn(terms["vb"])
terms["loss"] = terms["mse"] + mean_flat(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 = mean_flat(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 test_causal_training_losses():
from models.diffusion.respace import SpacedDiffusion
from models.diffusion.respace import space_timesteps
diff = SpacedDiffusion(use_timesteps=space_timesteps(4000, [4000]), model_mean_type='epsilon',
model_var_type='learned_range', loss_type='mse', betas=get_named_beta_schedule('linear', 4000),
conditioning_free=False, conditioning_free_k=1)
class IdentityTwoArg(torch.nn.Module):
def __init__(self):
super().__init__()
def forward(self, x, *args, **kwargs):
return x.repeat(1,2,1)
model = IdentityTwoArg()
diff.causal_training_losses(model, torch.randn(4,256,400), torch.tensor([500,1000,3000,3500]), causal_slope=4)
def graph_causal_timestep_adjustment():
import matplotlib.pyplot as plt
S = 400
#slope=4
num_timesteps=4000
for slpe in range(10, 400, 50):
slope = slpe / 10
t_res = []
for t in range(num_timesteps, -1, -num_timesteps//50):
T = causal_timestep_adjustment(torch.tensor([t]), S, num_timesteps, causal_slope=slope, add_jitter=False)[0]
# The following adjustment makes it easier to visualize the timestep regions where the model is actually working.
#T_adj = (T == num_timesteps).logical_or(T == -1)
#T[T_adj] = t
t_res.append(T)
plt.plot(T.numpy())
for i in range(len(t_res)):
for j in range(len(t_res)):
if i == j:
continue
assert not torch.all(t_res[i] == t_res[j])
plt.ylim(0,num_timesteps)
plt.xlim(0,4000)
plt.ylabel('timestep')
plt.savefig(f'{slpe}.png')
plt.clf()
def graph_causal_timestep_adjustment_by_timestep():
import matplotlib.pyplot as plt
S = 400
slope=8
num_timesteps=4000
t_res = []
for t in range(num_timesteps, -1, -num_timesteps//50):
T = causal_timestep_adjustment(torch.tensor([t]), S, num_timesteps, causal_slope=slope, add_jitter=False)[0]
t_res.append(T)
plt.plot(T.numpy())
plt.ylim(0,num_timesteps)
plt.xlim(0,4000)
plt.ylabel('timestep')
plt.savefig(f'{t}.png')
plt.clf()
if __name__ == '__main__':
#test_causal_training_losses()
#graph_causal_timestep_adjustment()
graph_causal_timestep_adjustment_by_timestep()