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karras_diffusion.py
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karras_diffusion.py
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"""
Based on: https://github.com/crowsonkb/k-diffusion
"""
import numpy as np
import torch as th
import torch.nn as nn
import torch.nn.functional as F
from piq import LPIPS
from .nn import mean_flat, append_dims, append_zero
from functools import partial
def vp_logsnr(t, beta_d, beta_min):
t = th.as_tensor(t)
return - th.log((0.5 * beta_d * (t ** 2) + beta_min * t).exp() - 1)
def vp_logs(t, beta_d, beta_min):
t = th.as_tensor(t)
return -0.25 * t ** 2 * (beta_d) - 0.5 * t * beta_min
class KarrasDenoiser:
def __init__(
self,
sigma_data: float = 0.5,
sigma_max=80.0,
sigma_min=0.002,
beta_d=2,
beta_min=0.1,
cov_xy=0., # 0 for uncorrelated, sigma_data**2 / 2 for C_skip=1/2 at sigma_max
rho=7.0,
image_size=64,
weight_schedule="karras",
pred_mode='both',
loss_norm="lpips",
):
self.sigma_data = sigma_data
self.sigma_max = sigma_max
self.sigma_min = sigma_min
self.beta_d = beta_d
self.beta_min = beta_min
self.sigma_data_end = self.sigma_data
self.cov_xy = cov_xy
self.c = 1
self.weight_schedule = weight_schedule
self.pred_mode = pred_mode
self.loss_norm = loss_norm
if loss_norm == "lpips":
self.lpips_loss = LPIPS(replace_pooling=True, reduction="none")
self.rho = rho
self.num_timesteps = 40
self.image_size = image_size
def get_snr(self, sigmas):
if self.pred_mode.startswith('vp'):
return vp_logsnr(sigmas, self.beta_d, self.beta_min).exp()
else:
return sigmas**-2
def get_sigmas(self, sigmas):
return sigmas
def get_weightings(self, sigma):
snrs = self.get_snr(sigma)
if self.weight_schedule == "snr":
weightings = snrs
elif self.weight_schedule == "snr+1":
weightings = snrs + 1
elif self.weight_schedule == "karras":
weightings = snrs + 1.0 / self.sigma_data**2
elif self.weight_schedule.startswith("bridge_karras"):
if self.pred_mode == 've':
A = sigma**4 / self.sigma_max**4 * self.sigma_data_end**2 + (1 - sigma**2 / self.sigma_max**2)**2 * self.sigma_data**2 + 2*sigma**2 / self.sigma_max**2 * (1 - sigma**2 / self.sigma_max**2) * self.cov_xy + self.c**2 * sigma**2 * (1 - sigma**2 / self.sigma_max**2)
weightings = A / ((sigma/self.sigma_max)**4 * (self.sigma_data_end**2 * self.sigma_data**2 - self.cov_xy**2) + self.sigma_data**2 * self.c**2 * sigma**2 * (1 - sigma**2/self.sigma_max**2) )
elif self.pred_mode == 'vp':
logsnr_t = vp_logsnr(sigma, self.beta_d, self.beta_min)
logsnr_T = vp_logsnr(1, self.beta_d, self.beta_min)
logs_t = vp_logs(sigma, self.beta_d, self.beta_min)
logs_T = vp_logs(1, self.beta_d, self.beta_min)
a_t = (logsnr_T - logsnr_t +logs_t -logs_T).exp()
b_t = -th.expm1(logsnr_T - logsnr_t) * logs_t.exp()
c_t = -th.expm1(logsnr_T - logsnr_t) * (2*logs_t - logsnr_t).exp()
A = a_t**2 * self.sigma_data_end**2 + b_t**2 * self.sigma_data**2 + 2*a_t * b_t * self.cov_xy + self.c**2 * c_t
weightings = A / (a_t**2 * (self.sigma_data_end**2 * self.sigma_data**2 - self.cov_xy**2) + self.sigma_data**2 * self.c**2 * c_t )
elif self.pred_mode == 'vp_simple' or self.pred_mode == 've_simple':
weightings = th.ones_like(snrs)
elif self.weight_schedule == "truncated-snr":
weightings = th.clamp(snrs, min=1.0)
elif self.weight_schedule == "uniform":
weightings = th.ones_like(snrs)
else:
raise NotImplementedError()
return weightings
def get_bridge_scalings(self, sigma):
if self.pred_mode == 've':
A = sigma**4 / self.sigma_max**4 * self.sigma_data_end**2 + (1 - sigma**2 / self.sigma_max**2)**2 * self.sigma_data**2 + 2*sigma**2 / self.sigma_max**2 * (1 - sigma**2 / self.sigma_max**2) * self.cov_xy + self.c **2 * sigma**2 * (1 - sigma**2 / self.sigma_max**2)
c_in = 1 / (A) ** 0.5
c_skip = ((1 - sigma**2 / self.sigma_max**2) * self.sigma_data**2 + sigma**2 / self.sigma_max**2 * self.cov_xy)/ A
c_out =((sigma/self.sigma_max)**4 * (self.sigma_data_end**2 * self.sigma_data**2 - self.cov_xy**2) + self.sigma_data**2 * self.c **2 * sigma**2 * (1 - sigma**2/self.sigma_max**2) )**0.5 * c_in
return c_skip, c_out, c_in
elif self.pred_mode == 'vp':
logsnr_t = vp_logsnr(sigma, self.beta_d, self.beta_min)
logsnr_T = vp_logsnr(1, self.beta_d, self.beta_min)
logs_t = vp_logs(sigma, self.beta_d, self.beta_min)
logs_T = vp_logs(1, self.beta_d, self.beta_min)
a_t = (logsnr_T - logsnr_t +logs_t -logs_T).exp()
b_t = -th.expm1(logsnr_T - logsnr_t) * logs_t.exp()
c_t = -th.expm1(logsnr_T - logsnr_t) * (2*logs_t - logsnr_t).exp()
A = a_t**2 * self.sigma_data_end**2 + b_t**2 * self.sigma_data**2 + 2*a_t * b_t * self.cov_xy + self.c**2 * c_t
c_in = 1 / (A) ** 0.5
c_skip = (b_t * self.sigma_data**2 + a_t * self.cov_xy)/ A
c_out =(a_t**2 * (self.sigma_data_end**2 * self.sigma_data**2 - self.cov_xy**2) + self.sigma_data**2 * self.c **2 * c_t )**0.5 * c_in
return c_skip, c_out, c_in
elif self.pred_mode == 've_simple' or self.pred_mode == 'vp_simple':
c_in = th.ones_like(sigma)
c_out = th.ones_like(sigma)
c_skip = th.zeros_like(sigma)
return c_skip, c_out, c_in
def training_bridge_losses(self, model, x_start, sigmas, model_kwargs=None, noise=None, vae=None):
assert model_kwargs is not None
xT = model_kwargs['xT']
if noise is None:
noise = th.randn_like(x_start)
sigmas =th.minimum(sigmas, th.ones_like(sigmas)* self.sigma_max)
terms = {}
dims = x_start.ndim
def bridge_sample(x0, xT, t):
t = append_dims(t, dims)
# std_t = th.sqrt(t)* th.sqrt(1 - t / self.sigma_max)
if self.pred_mode.startswith('ve'):
std_t = t* th.sqrt(1 - t**2 / self.sigma_max**2)
mu_t= t**2 / self.sigma_max**2 * xT + (1 - t**2 / self.sigma_max**2) * x0
samples = (mu_t + std_t * noise )
elif self.pred_mode.startswith('vp'):
logsnr_t = vp_logsnr(t, self.beta_d, self.beta_min)
logsnr_T = vp_logsnr(self.sigma_max, self.beta_d, self.beta_min)
logs_t = vp_logs(t, self.beta_d, self.beta_min)
logs_T = vp_logs(self.sigma_max, self.beta_d, self.beta_min)
a_t = (logsnr_T - logsnr_t +logs_t -logs_T).exp()
b_t = -th.expm1(logsnr_T - logsnr_t) * logs_t.exp()
std_t = (-th.expm1(logsnr_T - logsnr_t)).sqrt() * (logs_t - logsnr_t/2).exp()
samples= a_t * xT + b_t * x0 + std_t * noise
return samples
x_t = bridge_sample(x_start, xT, sigmas)
model_output, denoised = self.denoise(model, x_t, sigmas, **model_kwargs)
weights = self.get_weightings(sigmas)
weights = append_dims((weights), dims)
terms["xs_mse"] = mean_flat((denoised - x_start) ** 2)
terms["mse"] = mean_flat(weights * (denoised - x_start) ** 2)
if "vb" in terms:
terms["loss"] = terms["mse"] + terms["vb"]
else:
terms["loss"] = terms["mse"]
return terms
def denoise(self, model, x_t, sigmas ,**model_kwargs):
c_skip, c_out, c_in = [
append_dims(x, x_t.ndim) for x in self.get_bridge_scalings(sigmas)
]
rescaled_t = 1000 * 0.25 * th.log(sigmas + 1e-44)
model_output = model(c_in * x_t, rescaled_t, **model_kwargs)
denoised = c_out * model_output + c_skip * x_t
return model_output, denoised
def karras_sample(
diffusion,
model,
x_T,
x_0,
steps,
clip_denoised=True,
progress=False,
callback=None,
model_kwargs=None,
device=None,
sigma_min=0.002,
sigma_max=80, # higher for highres?
rho=7.0,
sampler="heun",
churn_step_ratio=0.,
guidance=1,
):
assert sampler in ["heun", ], 'only heun sampler is supported currently'
sigmas = get_sigmas_karras(steps, sigma_min, sigma_max-1e-4, rho, device=device)
sample_fn = {
"heun": partial(sample_heun, beta_d=diffusion.beta_d, beta_min=diffusion.beta_min),
}[sampler]
sampler_args = dict(
pred_mode=diffusion.pred_mode, churn_step_ratio=churn_step_ratio, sigma_max=sigma_max
)
def denoiser(x_t, sigma, x_T=None):
_, denoised = diffusion.denoise(model, x_t, sigma, **model_kwargs)
if clip_denoised:
denoised = denoised.clamp(-1, 1)
return denoised
x_0, path, nfe = sample_fn(
denoiser,
x_T,
sigmas,
progress=progress,
callback=callback,
guidance=guidance,
**sampler_args,
)
print('nfe:', nfe)
return x_0.clamp(-1, 1), [x.clamp(-1, 1) for x in path], nfe
def get_sigmas_karras(n, sigma_min, sigma_max, rho=7.0, device="cpu"):
"""Constructs the noise schedule of Karras et al. (2022)."""
ramp = th.linspace(0, 1, n)
min_inv_rho = sigma_min ** (1 / rho)
max_inv_rho = sigma_max ** (1 / rho)
sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
return append_zero(sigmas).to(device)
def get_bridge_sigmas_karras(n, sigma_min, sigma_max, rho=7.0, eps=1e-4, device="cpu"):
sigma_t_crit = sigma_max / np.sqrt(2)
min_start_inv_rho = sigma_min ** (1 / rho)
max_inv_rho = sigma_t_crit ** (1 / rho)
sigmas_second_half = (max_inv_rho + th.linspace(0, 1, n//2 ) * (min_start_inv_rho - max_inv_rho)) ** rho
sigmas_first_half = sigma_max - ((sigma_max - sigma_t_crit) ** (1 / rho) + th.linspace(0, 1, n - n//2 +1 ) * (eps ** (1 / rho) - (sigma_max - sigma_t_crit) ** (1 / rho))) ** rho
sigmas = th.cat([sigmas_first_half.flip(0)[:-1], sigmas_second_half])
sigmas_bridge = sigmas**2 *(1-sigmas**2/sigma_max**2)
return append_zero(sigmas).to(device)#, append_zero(sigmas_bridge).to(device)
def to_d(x, sigma, denoised, x_T, sigma_max, w=1, stochastic=False):
"""Converts a denoiser output to a Karras ODE derivative."""
grad_pxtlx0 = (denoised - x) / append_dims(sigma**2, x.ndim)
grad_pxTlxt = (x_T - x) / (append_dims(th.ones_like(sigma)*sigma_max**2, x.ndim) - append_dims(sigma**2, x.ndim))
gt2 = 2*sigma
d = - (0.5 if not stochastic else 1) * gt2 * (grad_pxtlx0 - w * grad_pxTlxt * (0 if stochastic else 1))
if stochastic:
return d, gt2
else:
return d
def get_d_vp(x, denoised, x_T, std_t,logsnr_t, logsnr_T, logs_t, logs_T, s_t_deriv, sigma_t, sigma_t_deriv, w, stochastic=False):
a_t = (logsnr_T - logsnr_t + logs_t - logs_T).exp()
b_t = -th.expm1(logsnr_T - logsnr_t) * logs_t.exp()
mu_t = a_t * x_T + b_t * denoised
grad_logq = - (x - mu_t)/std_t**2 / (-th.expm1(logsnr_T - logsnr_t))
# grad_logpxtlx0 = - (x - logs_t.exp()*denoised)/std_t**2
grad_logpxTlxt = -(x - th.exp(logs_t-logs_T)*x_T) /std_t**2 / th.expm1(logsnr_t - logsnr_T)
f = s_t_deriv * (-logs_t).exp() * x
gt2 = 2 * (logs_t).exp()**2 * sigma_t * sigma_t_deriv
# breakpoint()
d = f - gt2 * ((0.5 if not stochastic else 1)* grad_logq - w * grad_logpxTlxt)
# d = f - (0.5 if not stochastic else 1) * gt2 * (grad_logpxtlx0 - w * grad_logpxTlxt* (0 if stochastic else 1))
if stochastic:
return d, gt2
else:
return d
@th.no_grad()
def sample_heun(
denoiser,
x,
sigmas,
pred_mode='both',
progress=False,
callback=None,
sigma_max=80.0,
beta_d=2,
beta_min=0.1,
churn_step_ratio=0.,
guidance=1,
):
"""Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
x_T = x
path = [x]
s_in = x.new_ones([x.shape[0]])
indices = range(len(sigmas) - 1)
if progress:
from tqdm.auto import tqdm
indices = tqdm(indices)
nfe = 0
assert churn_step_ratio < 1
if pred_mode.startswith('vp'):
vp_snr_sqrt_reciprocal = lambda t: (np.e ** (0.5 * beta_d * (t ** 2) + beta_min * t) - 1) ** 0.5
vp_snr_sqrt_reciprocal_deriv = lambda t: 0.5 * (beta_min + beta_d * t) * (vp_snr_sqrt_reciprocal(t) + 1 / vp_snr_sqrt_reciprocal(t))
s = lambda t: (1 + vp_snr_sqrt_reciprocal(t) ** 2).rsqrt()
s_deriv = lambda t: -vp_snr_sqrt_reciprocal(t) * vp_snr_sqrt_reciprocal_deriv(t) * (s(t) ** 3)
logs = lambda t: -0.25 * t ** 2 * (beta_d) - 0.5 * t * beta_min
std = lambda t: vp_snr_sqrt_reciprocal(t) * s(t)
logsnr = lambda t : - 2 * th.log(vp_snr_sqrt_reciprocal(t))
logsnr_T = logsnr(th.as_tensor(sigma_max))
logs_T = logs(th.as_tensor(sigma_max))
for j, i in enumerate(indices):
if churn_step_ratio > 0:
# 1 step euler
sigma_hat = (sigmas[i+1] - sigmas[i]) * churn_step_ratio + sigmas[i]
denoised = denoiser(x, sigmas[i] * s_in, x_T)
if pred_mode == 've':
d_1, gt2 = to_d(x, sigmas[i] , denoised, x_T, sigma_max, w=guidance, stochastic=True)
elif pred_mode.startswith('vp'):
d_1, gt2 = get_d_vp(x, denoised, x_T, std(sigmas[i]),logsnr(sigmas[i]), logsnr_T, logs(sigmas[i] ), logs_T, s_deriv(sigmas[i] ), vp_snr_sqrt_reciprocal(sigmas[i] ), vp_snr_sqrt_reciprocal_deriv(sigmas[i] ), guidance, stochastic=True)
dt = (sigma_hat - sigmas[i])
x = x + d_1 * dt + th.randn_like(x) *((dt).abs() ** 0.5)*gt2.sqrt()
nfe += 1
path.append(x.detach().cpu())
else:
sigma_hat = sigmas[i]
# heun step
denoised = denoiser(x, sigma_hat * s_in, x_T)
if pred_mode == 've':
# d = (x - denoised ) / append_dims(sigma_hat, x.ndim)
d = to_d(x, sigma_hat, denoised, x_T, sigma_max, w=guidance)
elif pred_mode.startswith('vp'):
d = get_d_vp(x, denoised, x_T, std(sigma_hat),logsnr(sigma_hat), logsnr_T, logs(sigma_hat), logs_T, s_deriv(sigma_hat), vp_snr_sqrt_reciprocal(sigma_hat), vp_snr_sqrt_reciprocal_deriv(sigma_hat), guidance)
nfe += 1
if callback is not None:
callback(
{
"x": x,
"i": i,
"sigma": sigmas[i],
"sigma_hat": sigma_hat,
"denoised": denoised,
}
)
dt = sigmas[i + 1] - sigma_hat
if sigmas[i + 1] == 0:
x = x + d * dt
else:
# Heun's method
x_2 = x + d * dt
denoised_2 = denoiser(x_2, sigmas[i + 1] * s_in, x_T)
if pred_mode == 've':
# d_2 = (x_2 - denoised_2) / append_dims(sigmas[i + 1], x.ndim)
d_2 = to_d(x_2, sigmas[i + 1], denoised_2, x_T, sigma_max, w=guidance)
elif pred_mode.startswith('vp'):
d_2 = get_d_vp(x_2, denoised_2, x_T, std(sigmas[i + 1]),logsnr(sigmas[i + 1]), logsnr_T, logs(sigmas[i + 1]), logs_T, s_deriv(sigmas[i + 1]),
vp_snr_sqrt_reciprocal(sigmas[i + 1]), vp_snr_sqrt_reciprocal_deriv(sigmas[i + 1]), guidance)
d_prime = (d + d_2) / 2
# noise = th.zeros_like(x) if 'flow' in pred_mode or pred_mode == 'uncond' else generator.randn_like(x)
x = x + d_prime * dt #+ noise * (sigmas[i + 1]**2 - sigma_hat**2).abs() ** 0.5
nfe += 1
# loss = (denoised.detach().cpu() - x0).pow(2).mean().item()
# losses.append(loss)
path.append(x.detach().cpu())
return x, path, nfe
@th.no_grad()
def forward_sample(
x0,
y0,
sigma_max,
):
ts = th.linspace(0, sigma_max, 120)
x = x0
# for t, t_next in zip(ts[:-1], ts[1:]):
# grad_pxTlxt = (y0 - x) / (append_dims(th.ones_like(ts)*sigma_max**2, x.ndim) - append_dims(t**2, x.ndim))
# dt = (t_next - t)
# gt2 = 2*t
# x = x + grad_pxTlxt * dt + th.randn_like(x) *((dt).abs() ** 0.5)*gt2.sqrt()
path = [x]
for t in ts:
std_t = th.sqrt(t)* th.sqrt(1 - t / sigma_max)
mu_t= t / sigma_max * y0 + (1 - t / sigma_max) * x0
xt = (mu_t + std_t * th.randn_like(x0) )
path.append(xt)
path.append(y0)
return path