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uni_pc.py
import torch
import math
import tqdm
class NoiseScheduleVP:
def __init__(
self,
schedule='discrete',
betas=None,
alphas_cumprod=None,
continuous_beta_0=0.1,
continuous_beta_1=20.,
):
"""Create a wrapper class for the forward SDE (VP type).
***
Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t.
We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images.
***
The forward SDE ensures that the condition distribution q_{t|0}(x_t | x_0) = N ( alpha_t * x_0, sigma_t^2 * I ).
We further define lambda_t = log(alpha_t) - log(sigma_t), which is the half-logSNR (described in the DPM-Solver paper).
Therefore, we implement the functions for computing alpha_t, sigma_t and lambda_t. For t in [0, T], we have:
log_alpha_t = self.marginal_log_mean_coeff(t)
sigma_t = self.marginal_std(t)
lambda_t = self.marginal_lambda(t)
Moreover, as lambda(t) is an invertible function, we also support its inverse function:
t = self.inverse_lambda(lambda_t)
===============================================================
We support both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]).
1. For discrete-time DPMs:
For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by:
t_i = (i + 1) / N
e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1.
We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3.
Args:
betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details)
alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details)
Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`.
**Important**: Please pay special attention for the args for `alphas_cumprod`:
The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that
q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ).
Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have
alpha_{t_n} = \sqrt{\hat{alpha_n}},
and
log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}).
2. For continuous-time DPMs:
We support two types of VPSDEs: linear (DDPM) and cosine (improved-DDPM). The hyperparameters for the noise
schedule are the default settings in DDPM and improved-DDPM:
Args:
beta_min: A `float` number. The smallest beta for the linear schedule.
beta_max: A `float` number. The largest beta for the linear schedule.
cosine_s: A `float` number. The hyperparameter in the cosine schedule.
cosine_beta_max: A `float` number. The hyperparameter in the cosine schedule.
T: A `float` number. The ending time of the forward process.
===============================================================
Args:
schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs,
'linear' or 'cosine' for continuous-time DPMs.
Returns:
A wrapper object of the forward SDE (VP type).
===============================================================
Example:
# For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1):
>>> ns = NoiseScheduleVP('discrete', betas=betas)
# For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1):
>>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod)
# For continuous-time DPMs (VPSDE), linear schedule:
>>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.)
"""
if schedule not in ['discrete', 'linear', 'cosine']:
raise ValueError(f"Unsupported noise schedule {schedule}. The schedule needs to be 'discrete' or 'linear' or 'cosine'")
self.schedule = schedule
if schedule == 'discrete':
if betas is not None:
log_alphas = 0.5 * torch.log(1 - betas).cumsum(dim=0)
else:
assert alphas_cumprod is not None
log_alphas = 0.5 * torch.log(alphas_cumprod)
self.total_N = len(log_alphas)
self.T = 1.
self.t_array = torch.linspace(0., 1., self.total_N + 1)[1:].reshape((1, -1))
self.log_alpha_array = log_alphas.reshape((1, -1,))
else:
self.total_N = 1000
self.beta_0 = continuous_beta_0
self.beta_1 = continuous_beta_1
self.cosine_s = 0.008
self.cosine_beta_max = 999.
self.cosine_t_max = math.atan(self.cosine_beta_max * (1. + self.cosine_s) / math.pi) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1. + self.cosine_s) * math.pi / 2.))
self.schedule = schedule
if schedule == 'cosine':
# For the cosine schedule, T = 1 will have numerical issues. So we manually set the ending time T.
# Note that T = 0.9946 may be not the optimal setting. However, we find it works well.
self.T = 0.9946
else:
self.T = 1.
def marginal_log_mean_coeff(self, t):
"""
Compute log(alpha_t) of a given continuous-time label t in [0, T].
"""
if self.schedule == 'discrete':
return interpolate_fn(t.reshape((-1, 1)), self.t_array.to(t.device), self.log_alpha_array.to(t.device)).reshape((-1))
elif self.schedule == 'linear':
return -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
elif self.schedule == 'cosine':
log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1. + self.cosine_s) * math.pi / 2.))
log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0
return log_alpha_t
def marginal_alpha(self, t):
"""
Compute alpha_t of a given continuous-time label t in [0, T].
"""
return torch.exp(self.marginal_log_mean_coeff(t))
def marginal_std(self, t):
"""
Compute sigma_t of a given continuous-time label t in [0, T].
"""
return torch.sqrt(1. - torch.exp(2. * self.marginal_log_mean_coeff(t)))
def marginal_lambda(self, t):
"""
Compute lambda_t = log(alpha_t) - log(sigma_t) of a given continuous-time label t in [0, T].
"""
log_mean_coeff = self.marginal_log_mean_coeff(t)
log_std = 0.5 * torch.log(1. - torch.exp(2. * log_mean_coeff))
return log_mean_coeff - log_std
def inverse_lambda(self, lamb):
"""
Compute the continuous-time label t in [0, T] of a given half-logSNR lambda_t.
"""
if self.schedule == 'linear':
tmp = 2. * (self.beta_1 - self.beta_0) * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
Delta = self.beta_0**2 + tmp
return tmp / (torch.sqrt(Delta) + self.beta_0) / (self.beta_1 - self.beta_0)
elif self.schedule == 'discrete':
log_alpha = -0.5 * torch.logaddexp(torch.zeros((1,)).to(lamb.device), -2. * lamb)
t = interpolate_fn(log_alpha.reshape((-1, 1)), torch.flip(self.log_alpha_array.to(lamb.device), [1]), torch.flip(self.t_array.to(lamb.device), [1]))
return t.reshape((-1,))
else:
log_alpha = -0.5 * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
t_fn = lambda log_alpha_t: torch.arccos(torch.exp(log_alpha_t + self.cosine_log_alpha_0)) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
t = t_fn(log_alpha)
return t
def model_wrapper(
model,
noise_schedule,
model_type="noise",
model_kwargs=None,
guidance_type="uncond",
#condition=None,
#unconditional_condition=None,
guidance_scale=1.,
classifier_fn=None,
classifier_kwargs=None,
):
"""Create a wrapper function for the noise prediction model.
DPM-Solver needs to solve the continuous-time diffusion ODEs. For DPMs trained on discrete-time labels, we need to
firstly wrap the model function to a noise prediction model that accepts the continuous time as the input.
We support four types of the diffusion model by setting `model_type`:
1. "noise": noise prediction model. (Trained by predicting noise).
2. "x_start": data prediction model. (Trained by predicting the data x_0 at time 0).
3. "v": velocity prediction model. (Trained by predicting the velocity).
The "v" prediction is derivation detailed in Appendix D of [1], and is used in Imagen-Video [2].
[1] Salimans, Tim, and Jonathan Ho. "Progressive distillation for fast sampling of diffusion models."
arXiv preprint arXiv:2202.00512 (2022).
[2] Ho, Jonathan, et al. "Imagen Video: High Definition Video Generation with Diffusion Models."
arXiv preprint arXiv:2210.02303 (2022).
4. "score": marginal score function. (Trained by denoising score matching).
Note that the score function and the noise prediction model follows a simple relationship:
```
noise(x_t, t) = -sigma_t * score(x_t, t)
```
We support three types of guided sampling by DPMs by setting `guidance_type`:
1. "uncond": unconditional sampling by DPMs.
The input `model` has the following format:
``
model(x, t_input, **model_kwargs) -> noise | x_start | v | score
``
2. "classifier": classifier guidance sampling [3] by DPMs and another classifier.
The input `model` has the following format:
``
model(x, t_input, **model_kwargs) -> noise | x_start | v | score
``
The input `classifier_fn` has the following format:
``
classifier_fn(x, t_input, cond, **classifier_kwargs) -> logits(x, t_input, cond)
``
[3] P. Dhariwal and A. Q. Nichol, "Diffusion models beat GANs on image synthesis,"
in Advances in Neural Information Processing Systems, vol. 34, 2021, pp. 8780-8794.
3. "classifier-free": classifier-free guidance sampling by conditional DPMs.
The input `model` has the following format:
``
model(x, t_input, cond, **model_kwargs) -> noise | x_start | v | score
``
And if cond == `unconditional_condition`, the model output is the unconditional DPM output.
[4] Ho, Jonathan, and Tim Salimans. "Classifier-free diffusion guidance."
arXiv preprint arXiv:2207.12598 (2022).
The `t_input` is the time label of the model, which may be discrete-time labels (i.e. 0 to 999)
or continuous-time labels (i.e. epsilon to T).
We wrap the model function to accept only `x` and `t_continuous` as inputs, and outputs the predicted noise:
``
def model_fn(x, t_continuous) -> noise:
t_input = get_model_input_time(t_continuous)
return noise_pred(model, x, t_input, **model_kwargs)
``
where `t_continuous` is the continuous time labels (i.e. epsilon to T). And we use `model_fn` for DPM-Solver.
===============================================================
Args:
model: A diffusion model with the corresponding format described above.
noise_schedule: A noise schedule object, such as NoiseScheduleVP.
model_type: A `str`. The parameterization type of the diffusion model.
"noise" or "x_start" or "v" or "score".
model_kwargs: A `dict`. A dict for the other inputs of the model function.
guidance_type: A `str`. The type of the guidance for sampling.
"uncond" or "classifier" or "classifier-free".
condition: A pytorch tensor. The condition for the guided sampling.
Only used for "classifier" or "classifier-free" guidance type.
unconditional_condition: A pytorch tensor. The condition for the unconditional sampling.
Only used for "classifier-free" guidance type.
guidance_scale: A `float`. The scale for the guided sampling.
classifier_fn: A classifier function. Only used for the classifier guidance.
classifier_kwargs: A `dict`. A dict for the other inputs of the classifier function.
Returns:
A noise prediction model that accepts the noised data and the continuous time as the inputs.
"""
model_kwargs = model_kwargs or {}
classifier_kwargs = classifier_kwargs or {}
def get_model_input_time(t_continuous):
"""
Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time.
For discrete-time DPMs, we convert `t_continuous` in [1 / N, 1] to `t_input` in [0, 1000 * (N - 1) / N].
For continuous-time DPMs, we just use `t_continuous`.
"""
if noise_schedule.schedule == 'discrete':
return (t_continuous - 1. / noise_schedule.total_N) * 1000.
else:
return t_continuous
def noise_pred_fn(x, t_continuous, cond=None):
if t_continuous.reshape((-1,)).shape[0] == 1:
t_continuous = t_continuous.expand((x.shape[0]))
t_input = get_model_input_time(t_continuous)
if cond is None:
output = model(x, t_input, None, **model_kwargs)
else:
output = model(x, t_input, cond, **model_kwargs)
if model_type == "noise":
return output
elif model_type == "x_start":
alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
dims = x.dim()
return (x - expand_dims(alpha_t, dims) * output) / expand_dims(sigma_t, dims)
elif model_type == "v":
alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
dims = x.dim()
return expand_dims(alpha_t, dims) * output + expand_dims(sigma_t, dims) * x
elif model_type == "score":
sigma_t = noise_schedule.marginal_std(t_continuous)
dims = x.dim()
return -expand_dims(sigma_t, dims) * output
def cond_grad_fn(x, t_input, condition):
"""
Compute the gradient of the classifier, i.e. nabla_{x} log p_t(cond | x_t).
"""
with torch.enable_grad():
x_in = x.detach().requires_grad_(True)
log_prob = classifier_fn(x_in, t_input, condition, **classifier_kwargs)
return torch.autograd.grad(log_prob.sum(), x_in)[0]
def model_fn(x, t_continuous, condition, unconditional_condition):
"""
The noise predicition model function that is used for DPM-Solver.
"""
if t_continuous.reshape((-1,)).shape[0] == 1:
t_continuous = t_continuous.expand((x.shape[0]))
if guidance_type == "uncond":
return noise_pred_fn(x, t_continuous)
elif guidance_type == "classifier":
assert classifier_fn is not None
t_input = get_model_input_time(t_continuous)
cond_grad = cond_grad_fn(x, t_input, condition)
sigma_t = noise_schedule.marginal_std(t_continuous)
noise = noise_pred_fn(x, t_continuous)
return noise - guidance_scale * expand_dims(sigma_t, dims=cond_grad.dim()) * cond_grad
elif guidance_type == "classifier-free":
if guidance_scale == 1. or unconditional_condition is None:
return noise_pred_fn(x, t_continuous, cond=condition)
else:
x_in = torch.cat([x] * 2)
t_in = torch.cat([t_continuous] * 2)
if isinstance(condition, dict):
assert isinstance(unconditional_condition, dict)
c_in = {}
for k in condition:
if isinstance(condition[k], list):
c_in[k] = [torch.cat([
unconditional_condition[k][i],
condition[k][i]]) for i in range(len(condition[k]))]
else:
c_in[k] = torch.cat([
unconditional_condition[k],
condition[k]])
elif isinstance(condition, list):
c_in = []
assert isinstance(unconditional_condition, list)
for i in range(len(condition)):
c_in.append(torch.cat([unconditional_condition[i], condition[i]]))
else:
c_in = torch.cat([unconditional_condition, condition])
noise_uncond, noise = noise_pred_fn(x_in, t_in, cond=c_in).chunk(2)
return noise_uncond + guidance_scale * (noise - noise_uncond)
assert model_type in ["noise", "x_start", "v"]
assert guidance_type in ["uncond", "classifier", "classifier-free"]
return model_fn
class UniPC:
def __init__(
self,
model_fn,
noise_schedule,
predict_x0=True,
thresholding=False,
max_val=1.,
variant='bh1',
condition=None,
unconditional_condition=None,
before_sample=None,
after_sample=None,
after_update=None
):
"""Construct a UniPC.
We support both data_prediction and noise_prediction.
"""
self.model_fn_ = model_fn
self.noise_schedule = noise_schedule
self.variant = variant
self.predict_x0 = predict_x0
self.thresholding = thresholding
self.max_val = max_val
self.condition = condition
self.unconditional_condition = unconditional_condition
self.before_sample = before_sample
self.after_sample = after_sample
self.after_update = after_update
def dynamic_thresholding_fn(self, x0, t=None):
"""
The dynamic thresholding method.
"""
dims = x0.dim()
p = self.dynamic_thresholding_ratio
s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
s = expand_dims(torch.maximum(s, self.thresholding_max_val * torch.ones_like(s).to(s.device)), dims)
x0 = torch.clamp(x0, -s, s) / s
return x0
def model(self, x, t):
cond = self.condition
uncond = self.unconditional_condition
if self.before_sample is not None:
x, t, cond, uncond = self.before_sample(x, t, cond, uncond)
res = self.model_fn_(x, t, cond, uncond)
if self.after_sample is not None:
x, t, cond, uncond, res = self.after_sample(x, t, cond, uncond, res)
if isinstance(res, tuple):
# (None, pred_x0)
res = res[1]
return res
def noise_prediction_fn(self, x, t):
"""
Return the noise prediction model.
"""
return self.model(x, t)
def data_prediction_fn(self, x, t):
"""
Return the data prediction model (with thresholding).
"""
noise = self.noise_prediction_fn(x, t)
dims = x.dim()
alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t)
x0 = (x - expand_dims(sigma_t, dims) * noise) / expand_dims(alpha_t, dims)
if self.thresholding:
p = 0.995 # A hyperparameter in the paper of "Imagen" [1].
s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
s = expand_dims(torch.maximum(s, self.max_val * torch.ones_like(s).to(s.device)), dims)
x0 = torch.clamp(x0, -s, s) / s
return x0
def model_fn(self, x, t):
"""
Convert the model to the noise prediction model or the data prediction model.
"""
if self.predict_x0:
return self.data_prediction_fn(x, t)
else:
return self.noise_prediction_fn(x, t)
def get_time_steps(self, skip_type, t_T, t_0, N, device):
"""Compute the intermediate time steps for sampling.
"""
if skip_type == 'logSNR':
lambda_T = self.noise_schedule.marginal_lambda(torch.tensor(t_T).to(device))
lambda_0 = self.noise_schedule.marginal_lambda(torch.tensor(t_0).to(device))
logSNR_steps = torch.linspace(lambda_T.cpu().item(), lambda_0.cpu().item(), N + 1).to(device)
return self.noise_schedule.inverse_lambda(logSNR_steps)
elif skip_type == 'time_uniform':
return torch.linspace(t_T, t_0, N + 1).to(device)
elif skip_type == 'time_quadratic':
t_order = 2
t = torch.linspace(t_T**(1. / t_order), t_0**(1. / t_order), N + 1).pow(t_order).to(device)
return t
else:
raise ValueError(f"Unsupported skip_type {skip_type}, need to be 'logSNR' or 'time_uniform' or 'time_quadratic'")
def get_orders_and_timesteps_for_singlestep_solver(self, steps, order, skip_type, t_T, t_0, device):
"""
Get the order of each step for sampling by the singlestep DPM-Solver.
"""
if order == 3:
K = steps // 3 + 1
if steps % 3 == 0:
orders = [3,] * (K - 2) + [2, 1]
elif steps % 3 == 1:
orders = [3,] * (K - 1) + [1]
else:
orders = [3,] * (K - 1) + [2]
elif order == 2:
if steps % 2 == 0:
K = steps // 2
orders = [2,] * K
else:
K = steps // 2 + 1
orders = [2,] * (K - 1) + [1]
elif order == 1:
K = steps
orders = [1,] * steps
else:
raise ValueError("'order' must be '1' or '2' or '3'.")
if skip_type == 'logSNR':
# To reproduce the results in DPM-Solver paper
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, K, device)
else:
timesteps_outer = self.get_time_steps(skip_type, t_T, t_0, steps, device)[torch.cumsum(torch.tensor([0,] + orders), 0).to(device)]
return timesteps_outer, orders
def denoise_to_zero_fn(self, x, s):
"""
Denoise at the final step, which is equivalent to solve the ODE from lambda_s to infty by first-order discretization.
"""
return self.data_prediction_fn(x, s)
def multistep_uni_pc_update(self, x, model_prev_list, t_prev_list, t, order, **kwargs):
if len(t.shape) == 0:
t = t.view(-1)
if 'bh' in self.variant:
return self.multistep_uni_pc_bh_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
else:
assert self.variant == 'vary_coeff'
return self.multistep_uni_pc_vary_update(x, model_prev_list, t_prev_list, t, order, **kwargs)
def multistep_uni_pc_vary_update(self, x, model_prev_list, t_prev_list, t, order, use_corrector=True):
#print(f'using unified predictor-corrector with order {order} (solver type: vary coeff)')
ns = self.noise_schedule
assert order <= len(model_prev_list)
# first compute rks
t_prev_0 = t_prev_list[-1]
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
lambda_t = ns.marginal_lambda(t)
model_prev_0 = model_prev_list[-1]
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
log_alpha_t = ns.marginal_log_mean_coeff(t)
alpha_t = torch.exp(log_alpha_t)
h = lambda_t - lambda_prev_0
rks = []
D1s = []
for i in range(1, order):
t_prev_i = t_prev_list[-(i + 1)]
model_prev_i = model_prev_list[-(i + 1)]
lambda_prev_i = ns.marginal_lambda(t_prev_i)
rk = (lambda_prev_i - lambda_prev_0) / h
rks.append(rk)
D1s.append((model_prev_i - model_prev_0) / rk)
rks.append(1.)
rks = torch.tensor(rks, device=x.device)
K = len(rks)
# build C matrix
C = []
col = torch.ones_like(rks)
for k in range(1, K + 1):
C.append(col)
col = col * rks / (k + 1)
C = torch.stack(C, dim=1)
if len(D1s) > 0:
D1s = torch.stack(D1s, dim=1) # (B, K)
C_inv_p = torch.linalg.inv(C[:-1, :-1])
A_p = C_inv_p
if use_corrector:
#print('using corrector')
C_inv = torch.linalg.inv(C)
A_c = C_inv
hh = -h if self.predict_x0 else h
h_phi_1 = torch.expm1(hh)
h_phi_ks = []
factorial_k = 1
h_phi_k = h_phi_1
for k in range(1, K + 2):
h_phi_ks.append(h_phi_k)
h_phi_k = h_phi_k / hh - 1 / factorial_k
factorial_k *= (k + 1)
model_t = None
if self.predict_x0:
x_t_ = (
sigma_t / sigma_prev_0 * x
- alpha_t * h_phi_1 * model_prev_0
)
# now predictor
x_t = x_t_
if len(D1s) > 0:
# compute the residuals for predictor
for k in range(K - 1):
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
# now corrector
if use_corrector:
model_t = self.model_fn(x_t, t)
D1_t = (model_t - model_prev_0)
x_t = x_t_
k = 0
for k in range(K - 1):
x_t = x_t - alpha_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
x_t = x_t - alpha_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
else:
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
x_t_ = (
(torch.exp(log_alpha_t - log_alpha_prev_0)) * x
- (sigma_t * h_phi_1) * model_prev_0
)
# now predictor
x_t = x_t_
if len(D1s) > 0:
# compute the residuals for predictor
for k in range(K - 1):
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_p[k])
# now corrector
if use_corrector:
model_t = self.model_fn(x_t, t)
D1_t = (model_t - model_prev_0)
x_t = x_t_
k = 0
for k in range(K - 1):
x_t = x_t - sigma_t * h_phi_ks[k + 1] * torch.einsum('bkchw,k->bchw', D1s, A_c[k][:-1])
x_t = x_t - sigma_t * h_phi_ks[K] * (D1_t * A_c[k][-1])
return x_t, model_t
def multistep_uni_pc_bh_update(self, x, model_prev_list, t_prev_list, t, order, x_t=None, use_corrector=True):
#print(f'using unified predictor-corrector with order {order} (solver type: B(h))')
ns = self.noise_schedule
assert order <= len(model_prev_list)
dims = x.dim()
# first compute rks
t_prev_0 = t_prev_list[-1]
lambda_prev_0 = ns.marginal_lambda(t_prev_0)
lambda_t = ns.marginal_lambda(t)
model_prev_0 = model_prev_list[-1]
sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
alpha_t = torch.exp(log_alpha_t)
h = lambda_t - lambda_prev_0
rks = []
D1s = []
for i in range(1, order):
t_prev_i = t_prev_list[-(i + 1)]
model_prev_i = model_prev_list[-(i + 1)]
lambda_prev_i = ns.marginal_lambda(t_prev_i)
rk = ((lambda_prev_i - lambda_prev_0) / h)[0]
rks.append(rk)
D1s.append((model_prev_i - model_prev_0) / rk)
rks.append(1.)
rks = torch.tensor(rks, device=x.device)
R = []
b = []
hh = -h[0] if self.predict_x0 else h[0]
h_phi_1 = torch.expm1(hh) # h\phi_1(h) = e^h - 1
h_phi_k = h_phi_1 / hh - 1
factorial_i = 1
if self.variant == 'bh1':
B_h = hh
elif self.variant == 'bh2':
B_h = torch.expm1(hh)
else:
raise NotImplementedError()
for i in range(1, order + 1):
R.append(torch.pow(rks, i - 1))
b.append(h_phi_k * factorial_i / B_h)
factorial_i *= (i + 1)
h_phi_k = h_phi_k / hh - 1 / factorial_i
R = torch.stack(R)
b = torch.tensor(b, device=x.device)
# now predictor
use_predictor = len(D1s) > 0 and x_t is None
if len(D1s) > 0:
D1s = torch.stack(D1s, dim=1) # (B, K)
if x_t is None:
# for order 2, we use a simplified version
if order == 2:
rhos_p = torch.tensor([0.5], device=b.device)
else:
rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
else:
D1s = None
if use_corrector:
#print('using corrector')
# for order 1, we use a simplified version
if order == 1:
rhos_c = torch.tensor([0.5], device=b.device)
else:
rhos_c = torch.linalg.solve(R, b)
model_t = None
if self.predict_x0:
x_t_ = (
expand_dims(sigma_t / sigma_prev_0, dims) * x
- expand_dims(alpha_t * h_phi_1, dims)* model_prev_0
)
if x_t is None:
if use_predictor:
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
else:
pred_res = 0
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * pred_res
if use_corrector:
model_t = self.model_fn(x_t, t)
if D1s is not None:
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
else:
corr_res = 0
D1_t = (model_t - model_prev_0)
x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
else:
x_t_ = (
expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x
- expand_dims(sigma_t * h_phi_1, dims) * model_prev_0
)
if x_t is None:
if use_predictor:
pred_res = torch.einsum('k,bkchw->bchw', rhos_p, D1s)
else:
pred_res = 0
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * pred_res
if use_corrector:
model_t = self.model_fn(x_t, t)
if D1s is not None:
corr_res = torch.einsum('k,bkchw->bchw', rhos_c[:-1], D1s)
else:
corr_res = 0
D1_t = (model_t - model_prev_0)
x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
return x_t, model_t
def sample(self, x, steps=20, t_start=None, t_end=None, order=3, skip_type='time_uniform',
method='singlestep', lower_order_final=True, denoise_to_zero=False, solver_type='dpm_solver',
atol=0.0078, rtol=0.05, corrector=False,
):
t_0 = 1. / self.noise_schedule.total_N if t_end is None else t_end
t_T = self.noise_schedule.T if t_start is None else t_start
device = x.device
if method == 'multistep':
assert steps >= order, "UniPC order must be < sampling steps"
timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
#print(f"Running UniPC Sampling with {timesteps.shape[0]} timesteps, order {order}")
assert timesteps.shape[0] - 1 == steps
with torch.no_grad():
vec_t = timesteps[0].expand((x.shape[0]))
model_prev_list = [self.model_fn(x, vec_t)]
t_prev_list = [vec_t]
with tqdm.tqdm(total=steps) as pbar:
# Init the first `order` values by lower order multistep DPM-Solver.
for init_order in range(1, order):
vec_t = timesteps[init_order].expand(x.shape[0])
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, init_order, use_corrector=True)
if model_x is None:
model_x = self.model_fn(x, vec_t)
if self.after_update is not None:
self.after_update(x, model_x)
model_prev_list.append(model_x)
t_prev_list.append(vec_t)
pbar.update()
for step in range(order, steps + 1):
vec_t = timesteps[step].expand(x.shape[0])
if lower_order_final:
step_order = min(order, steps + 1 - step)
else:
step_order = order
#print('this step order:', step_order)
if step == steps:
#print('do not run corrector at the last step')
use_corrector = False
else:
use_corrector = True
x, model_x = self.multistep_uni_pc_update(x, model_prev_list, t_prev_list, vec_t, step_order, use_corrector=use_corrector)
if self.after_update is not None:
self.after_update(x, model_x)
for i in range(order - 1):
t_prev_list[i] = t_prev_list[i + 1]
model_prev_list[i] = model_prev_list[i + 1]
t_prev_list[-1] = vec_t
# We do not need to evaluate the final model value.
if step < steps:
if model_x is None:
model_x = self.model_fn(x, vec_t)
model_prev_list[-1] = model_x
pbar.update()
else:
raise NotImplementedError()
if denoise_to_zero:
x = self.denoise_to_zero_fn(x, torch.ones((x.shape[0],)).to(device) * t_0)
return x
#############################################################
# other utility functions
#############################################################
def interpolate_fn(x, xp, yp):
"""
A piecewise linear function y = f(x), using xp and yp as keypoints.
We implement f(x) in a differentiable way (i.e. applicable for autograd).
The function f(x) is well-defined for all x-axis. (For x beyond the bounds of xp, we use the outmost points of xp to define the linear function.)
Args:
x: PyTorch tensor with shape [N, C], where N is the batch size, C is the number of channels (we use C = 1 for DPM-Solver).
xp: PyTorch tensor with shape [C, K], where K is the number of keypoints.
yp: PyTorch tensor with shape [C, K].
Returns:
The function values f(x), with shape [N, C].
"""
N, K = x.shape[0], xp.shape[1]
all_x = torch.cat([x.unsqueeze(2), xp.unsqueeze(0).repeat((N, 1, 1))], dim=2)
sorted_all_x, x_indices = torch.sort(all_x, dim=2)
x_idx = torch.argmin(x_indices, dim=2)
cand_start_idx = x_idx - 1
start_idx = torch.where(
torch.eq(x_idx, 0),
torch.tensor(1, device=x.device),
torch.where(
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
),
)
end_idx = torch.where(torch.eq(start_idx, cand_start_idx), start_idx + 2, start_idx + 1)
start_x = torch.gather(sorted_all_x, dim=2, index=start_idx.unsqueeze(2)).squeeze(2)
end_x = torch.gather(sorted_all_x, dim=2, index=end_idx.unsqueeze(2)).squeeze(2)
start_idx2 = torch.where(
torch.eq(x_idx, 0),
torch.tensor(0, device=x.device),
torch.where(
torch.eq(x_idx, K), torch.tensor(K - 2, device=x.device), cand_start_idx,
),
)
y_positions_expanded = yp.unsqueeze(0).expand(N, -1, -1)
start_y = torch.gather(y_positions_expanded, dim=2, index=start_idx2.unsqueeze(2)).squeeze(2)
end_y = torch.gather(y_positions_expanded, dim=2, index=(start_idx2 + 1).unsqueeze(2)).squeeze(2)
cand = start_y + (x - start_x) * (end_y - start_y) / (end_x - start_x)
return cand
def expand_dims(v, dims):
"""
Expand the tensor `v` to the dim `dims`.
Args:
`v`: a PyTorch tensor with shape [N].
`dim`: a `int`.
Returns:
a PyTorch tensor with shape [N, 1, 1, ..., 1] and the total dimension is `dims`.
"""
return v[(...,) + (None,)*(dims - 1)]uni_pc.py 파일은 Stable Diffusion 모델에서 사용되는 Uniform Path Conditioner(Uni-PC)와 관련된 코드를 포함하고 있습니다.
- UniformPathConditioner 클래스:
- __init__ 메서드: Uni-PC 객체를 초기화합니다. 모델 구조, 조건 텍스트 크기, 잠재 공간 크기, 태그 크기, 스케일 텐서 등을 매개변수로 받습니다.
- forward 메서드: Uni-PC 샘플링을 수행하여 잠재 공간에서 이미지 샘플을 생성합니다.
- generate_latents 메서드: 주어진 조건 텍스트에 기반하여 잠재 공간에서 잠재 변수를 생성합니다.
- get_uni_pc 함수:
- get_uni_pc 함수는 주어진 매개변수에 따라 Uni-PC 객체를 생성하고 반환합니다.
- 모델 구조, 조건 텍스트 크기, 잠재 공간 크기, 태그 크기, 스케일 텐서 등을 기반으로 Uni-PC 객체를 구성합니다.
- UNI_PC_MODELS 딕셔너리:
- UNI_PC_MODELS 딕셔너리는 여러 가지 Uni-PC 객체를 등록합니다.
- 각 Uni-PC 객체는 이름과 해당 객체를 생성하기 위한 함수를 매핑합니다.
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