import torch
import os
import PIL
from typing import List, Optional, Union
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from PIL import Image
from diffusers.utils import logging
VECTOR_DATA_FOLDER = "vector_data"
VECTOR_DATA_DICT = "vector_data"
logger = logging.get_logger(__name__)
def get_ddpm_inversion_scheduler(
scheduler,
step_function,
config,
timesteps,
save_timesteps,
latents,
x_ts,
x_ts_c_hat,
save_intermediate_results,
pipe,
x_0,
v1s_images,
v2s_images,
deltas_images,
v1_x0s,
v2_x0s,
deltas_x0s,
folder_name,
image_name,
time_measure_n,
):
def step(
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
variance_noise: Optional[torch.FloatTensor] = None,
return_dict: bool = True,
):
# if scheduler.is_save:
# start = timer()
res_inv = step_save_latents(
scheduler,
model_output[:1, :, :, :],
timestep,
sample[:1, :, :, :],
eta,
use_clipped_model_output,
generator,
variance_noise,
return_dict,
)
# end = timer()
# print(f"Run Time Inv: {end - start}")
res_inf = step_use_latents(
scheduler,
model_output[1:, :, :, :],
timestep,
sample[1:, :, :, :],
eta,
use_clipped_model_output,
generator,
variance_noise,
return_dict,
)
# res = res_inv
res = (torch.cat((res_inv[0], res_inf[0]), dim=0),)
return res
# return res
scheduler.step_function = step_function
scheduler.is_save = True
scheduler._timesteps = timesteps
scheduler._save_timesteps = save_timesteps if save_timesteps else timesteps
scheduler._config = config
scheduler.latents = latents
scheduler.x_ts = x_ts
scheduler.x_ts_c_hat = x_ts_c_hat
scheduler.step = step
scheduler.save_intermediate_results = save_intermediate_results
scheduler.pipe = pipe
scheduler.v1s_images = v1s_images
scheduler.v2s_images = v2s_images
scheduler.deltas_images = deltas_images
scheduler.v1_x0s = v1_x0s
scheduler.v2_x0s = v2_x0s
scheduler.deltas_x0s = deltas_x0s
scheduler.clean_step_run = False
scheduler.x_0s = create_xts(
config.noise_shift_delta,
config.noise_timesteps,
config.clean_step_timestep,
None,
pipe.scheduler,
timesteps,
x_0,
no_add_noise=True,
)
scheduler.folder_name = folder_name
scheduler.image_name = image_name
scheduler.p_to_p = False
scheduler.p_to_p_replace = False
scheduler.time_measure_n = time_measure_n
return scheduler
def step_save_latents(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
variance_noise: Optional[torch.FloatTensor] = None,
return_dict: bool = True,
):
# print(self._save_timesteps)
# timestep_index = map_timpstep_to_index[timestep]
# timestep_index = ((self._save_timesteps == timestep).nonzero(as_tuple=True)[0]).item()
timestep_index = self._save_timesteps.index(timestep) if not self.clean_step_run else -1
next_timestep_index = timestep_index + 1 if not self.clean_step_run else -1
u_hat_t = self.step_function(
model_output=model_output,
timestep=timestep,
sample=sample,
eta=eta,
use_clipped_model_output=use_clipped_model_output,
generator=generator,
variance_noise=variance_noise,
return_dict=False,
scheduler=self,
)
x_t_minus_1 = self.x_ts[next_timestep_index]
self.x_ts_c_hat.append(u_hat_t)
z_t = x_t_minus_1 - u_hat_t
self.latents.append(z_t)
z_t, _ = normalize(z_t, timestep_index, self._config.max_norm_zs)
x_t_minus_1_predicted = u_hat_t + z_t
if not return_dict:
return (x_t_minus_1_predicted,)
return DDIMSchedulerOutput(prev_sample=x_t_minus_1, pred_original_sample=None)
def step_use_latents(
self,
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
variance_noise: Optional[torch.FloatTensor] = None,
return_dict: bool = True,
):
# timestep_index = ((self._save_timesteps == timestep).nonzero(as_tuple=True)[0]).item()
timestep_index = self._timesteps.index(timestep) if not self.clean_step_run else -1
next_timestep_index = (
timestep_index + 1 if not self.clean_step_run else -1
)
z_t = self.latents[next_timestep_index] # + 1 because latents[0] is X_T
_, normalize_coefficient = normalize(
z_t[0] if self._config.breakdown == "x_t_hat_c_with_zeros" else z_t,
timestep_index,
self._config.max_norm_zs,
)
if normalize_coefficient == 0:
eta = 0
# eta = normalize_coefficient
x_t_hat_c_hat = self.step_function(
model_output=model_output,
timestep=timestep,
sample=sample,
eta=eta,
use_clipped_model_output=use_clipped_model_output,
generator=generator,
variance_noise=variance_noise,
return_dict=False,
scheduler=self,
)
w1 = self._config.ws1[timestep_index]
w2 = self._config.ws2[timestep_index]
x_t_minus_1_exact = self.x_ts[next_timestep_index]
x_t_minus_1_exact = x_t_minus_1_exact.expand_as(x_t_hat_c_hat)
x_t_c_hat: torch.Tensor = self.x_ts_c_hat[next_timestep_index]
if self._config.breakdown == "x_t_c_hat":
raise NotImplementedError("breakdown x_t_c_hat not implemented yet")
# x_t_c_hat = x_t_c_hat.expand_as(x_t_hat_c_hat)
x_t_c = x_t_c_hat[0].expand_as(x_t_hat_c_hat)
# if self._config.breakdown == "x_t_c_hat":
# v1 = x_t_hat_c_hat - x_t_c_hat
# v2 = x_t_c_hat - x_t_c
if (
self._config.breakdown == "x_t_hat_c"
or self._config.breakdown == "x_t_hat_c_with_zeros"
):
zero_index_reconstruction = 1 if not self.time_measure_n else 0
edit_prompts_num = (
(model_output.size(0) - zero_index_reconstruction) // 3
if self._config.breakdown == "x_t_hat_c_with_zeros" and not self.p_to_p
else (model_output.size(0) - zero_index_reconstruction) // 2
)
x_t_hat_c_indices = (zero_index_reconstruction, edit_prompts_num + zero_index_reconstruction)
edit_images_indices = (
edit_prompts_num + zero_index_reconstruction,
(
model_output.size(0)
if self._config.breakdown == "x_t_hat_c"
else zero_index_reconstruction + 2 * edit_prompts_num
),
)
x_t_hat_c = torch.zeros_like(x_t_hat_c_hat)
x_t_hat_c[edit_images_indices[0] : edit_images_indices[1]] = x_t_hat_c_hat[
x_t_hat_c_indices[0] : x_t_hat_c_indices[1]
]
v1 = x_t_hat_c_hat - x_t_hat_c
v2 = x_t_hat_c - normalize_coefficient * x_t_c
if self._config.breakdown == "x_t_hat_c_with_zeros" and not self.p_to_p:
path = os.path.join(
self.folder_name,
VECTOR_DATA_FOLDER,
self.image_name,
)
if not hasattr(self, VECTOR_DATA_DICT):
os.makedirs(path, exist_ok=True)
self.vector_data = dict()
x_t_0 = x_t_c_hat[1]
empty_prompt_indices = (1 + 2 * edit_prompts_num, 1 + 3 * edit_prompts_num)
x_t_hat_0 = x_t_hat_c_hat[empty_prompt_indices[0] : empty_prompt_indices[1]]
self.vector_data[timestep.item()] = dict()
self.vector_data[timestep.item()]["x_t_hat_c"] = x_t_hat_c[
edit_images_indices[0] : edit_images_indices[1]
]
self.vector_data[timestep.item()]["x_t_hat_0"] = x_t_hat_0
self.vector_data[timestep.item()]["x_t_c"] = x_t_c[0].expand_as(x_t_hat_0)
self.vector_data[timestep.item()]["x_t_0"] = x_t_0.expand_as(x_t_hat_0)
self.vector_data[timestep.item()]["x_t_hat_c_hat"] = x_t_hat_c_hat[
edit_images_indices[0] : edit_images_indices[1]
]
self.vector_data[timestep.item()]["x_t_minus_1_noisy"] = x_t_minus_1_exact[
0
].expand_as(x_t_hat_0)
self.vector_data[timestep.item()]["x_t_minus_1_clean"] = self.x_0s[
next_timestep_index
].expand_as(x_t_hat_0)
else: # no breakdown
v1 = x_t_hat_c_hat - normalize_coefficient * x_t_c
v2 = 0
if self.save_intermediate_results and not self.p_to_p:
delta = v1 + v2
v1_plus_x0 = self.x_0s[next_timestep_index] + v1
v2_plus_x0 = self.x_0s[next_timestep_index] + v2
delta_plus_x0 = self.x_0s[next_timestep_index] + delta
v1_images = decode_latents(v1, self.pipe)
self.v1s_images.append(v1_images)
v2_images = (
decode_latents(v2, self.pipe)
if self._config.breakdown != "no_breakdown"
else [PIL.Image.new("RGB", (1, 1))]
)
self.v2s_images.append(v2_images)
delta_images = decode_latents(delta, self.pipe)
self.deltas_images.append(delta_images)
v1_plus_x0_images = decode_latents(v1_plus_x0, self.pipe)
self.v1_x0s.append(v1_plus_x0_images)
v2_plus_x0_images = (
decode_latents(v2_plus_x0, self.pipe)
if self._config.breakdown != "no_breakdown"
else [PIL.Image.new("RGB", (1, 1))]
)
self.v2_x0s.append(v2_plus_x0_images)
delta_plus_x0_images = decode_latents(delta_plus_x0, self.pipe)
self.deltas_x0s.append(delta_plus_x0_images)
# print(f"v1 norm: {torch.norm(v1, dim=0).mean()}")
# if self._config.breakdown != "no_breakdown":
# print(f"v2 norm: {torch.norm(v2, dim=0).mean()}")
# print(f"v sum norm: {torch.norm(v1 + v2, dim=0).mean()}")
x_t_minus_1 = normalize_coefficient * x_t_minus_1_exact + w1 * v1 + w2 * v2
if (
self._config.breakdown == "x_t_hat_c"
or self._config.breakdown == "x_t_hat_c_with_zeros"
):
x_t_minus_1[x_t_hat_c_indices[0] : x_t_hat_c_indices[1]] = x_t_minus_1[
edit_images_indices[0] : edit_images_indices[1]
] # update x_t_hat_c to be x_t_hat_c_hat
if self._config.breakdown == "x_t_hat_c_with_zeros" and not self.p_to_p:
x_t_minus_1[empty_prompt_indices[0] : empty_prompt_indices[1]] = (
x_t_minus_1[edit_images_indices[0] : edit_images_indices[1]]
)
self.vector_data[timestep.item()]["x_t_minus_1_edited"] = x_t_minus_1[
edit_images_indices[0] : edit_images_indices[1]
]
if timestep == self._timesteps[-1]:
torch.save(
self.vector_data,
os.path.join(
path,
f"{VECTOR_DATA_DICT}.pt",
),
)
# p_to_p_force_perfect_reconstruction
if not self.time_measure_n:
x_t_minus_1[0] = x_t_minus_1_exact[0]
if not return_dict:
return (x_t_minus_1,)
return DDIMSchedulerOutput(
prev_sample=x_t_minus_1,
pred_original_sample=None,
)
def create_xts(
noise_shift_delta,
noise_timesteps,
clean_step_timestep,
generator,
scheduler,
timesteps,
x_0,
no_add_noise=False,
):
if noise_timesteps is None:
noising_delta = noise_shift_delta * (timesteps[0] - timesteps[1])
noise_timesteps = [timestep - int(noising_delta) for timestep in timesteps]
first_x_0_idx = len(noise_timesteps)
for i in range(len(noise_timesteps)):
if noise_timesteps[i] <= 0:
first_x_0_idx = i
break
noise_timesteps = noise_timesteps[:first_x_0_idx]
x_0_expanded = x_0.expand(len(noise_timesteps), -1, -1, -1)
noise = (
torch.randn(x_0_expanded.size(), generator=generator, device="cpu").to(
x_0.device
)
if not no_add_noise
else torch.zeros_like(x_0_expanded)
)
x_ts = scheduler.add_noise(
x_0_expanded,
noise,
torch.IntTensor(noise_timesteps),
)
x_ts = [t.unsqueeze(dim=0) for t in list(x_ts)]
x_ts += [x_0] * (len(timesteps) - first_x_0_idx)
x_ts += [x_0]
if clean_step_timestep > 0:
x_ts += [x_0]
return x_ts
def normalize(
z_t,
i,
max_norm_zs,
):
max_norm = max_norm_zs[i]
if max_norm < 0:
return z_t, 1
norm = torch.norm(z_t)
if norm < max_norm:
return z_t, 1
coeff = max_norm / norm
z_t = z_t * coeff
return z_t, coeff
def decode_latents(latent, pipe):
latent_img = pipe.vae.decode(
latent / pipe.vae.config.scaling_factor, return_dict=False
)[0]
return pipe.image_processor.postprocess(latent_img, output_type="pil")
def deterministic_ddim_step(
model_output: torch.FloatTensor,
timestep: int,
sample: torch.FloatTensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
generator=None,
variance_noise: Optional[torch.FloatTensor] = None,
return_dict: bool = True,
scheduler=None,
):
if scheduler.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
)
prev_timestep = (
timestep - scheduler.config.num_train_timesteps // scheduler.num_inference_steps
)
# 2. compute alphas, betas
alpha_prod_t = scheduler.alphas_cumprod[timestep]
alpha_prod_t_prev = (
scheduler.alphas_cumprod[prev_timestep]
if prev_timestep >= 0
else scheduler.final_alpha_cumprod
)
beta_prod_t = 1 - alpha_prod_t
if scheduler.config.prediction_type == "epsilon":
pred_original_sample = (
sample - beta_prod_t ** (0.5) * model_output
) / alpha_prod_t ** (0.5)
pred_epsilon = model_output
elif scheduler.config.prediction_type == "sample":
pred_original_sample = model_output
pred_epsilon = (
sample - alpha_prod_t ** (0.5) * pred_original_sample
) / beta_prod_t ** (0.5)
elif scheduler.config.prediction_type == "v_prediction":
pred_original_sample = (alpha_prod_t**0.5) * sample - (
beta_prod_t**0.5
) * model_output
pred_epsilon = (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
else:
raise ValueError(
f"prediction_type given as {scheduler.config.prediction_type} must be one of `epsilon`, `sample`, or"
" `v_prediction`"
)
# 4. Clip or threshold "predicted x_0"
if scheduler.config.thresholding:
pred_original_sample = scheduler._threshold_sample(pred_original_sample)
elif scheduler.config.clip_sample:
pred_original_sample = pred_original_sample.clamp(
-scheduler.config.clip_sample_range,
scheduler.config.clip_sample_range,
)
# 5. compute variance: "sigma_t(η)" -> see formula (16)
# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
variance = scheduler._get_variance(timestep, prev_timestep)
std_dev_t = eta * variance ** (0.5)
if use_clipped_model_output:
# the pred_epsilon is always re-derived from the clipped x_0 in Glide
pred_epsilon = (
sample - alpha_prod_t ** (0.5) * pred_original_sample
) / beta_prod_t ** (0.5)
# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (
0.5
) * pred_epsilon
# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
prev_sample = (
alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
)
return prev_sample
def deterministic_euler_step(
model_output: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
sample: torch.FloatTensor,
eta,
use_clipped_model_output,
generator,
variance_noise,
return_dict,
scheduler,
):
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
process from the learned model outputs (most often the predicted noise).
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
generator (`torch.Generator`, *optional*):
A random number generator.
return_dict (`bool`):
Whether or not to return a
[`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or tuple.
Returns:
[`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] or `tuple`:
If return_dict is `True`,
[`~schedulers.scheduling_euler_ancestral_discrete.EulerAncestralDiscreteSchedulerOutput`] is returned,
otherwise a tuple is returned where the first element is the sample tensor.
"""
if (
isinstance(timestep, int)
or isinstance(timestep, torch.IntTensor)
or isinstance(timestep, torch.LongTensor)
):
raise ValueError(
(
"Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
" `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
" one of the `scheduler.timesteps` as a timestep."
),
)
if scheduler.step_index is None:
scheduler._init_step_index(timestep)
sigma = scheduler.sigmas[scheduler.step_index]
# Upcast to avoid precision issues when computing prev_sample
sample = sample.to(torch.float32)
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
if scheduler.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma * model_output
elif scheduler.config.prediction_type == "v_prediction":
# * c_out + input * c_skip
pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (
sample / (sigma**2 + 1)
)
elif scheduler.config.prediction_type == "sample":
raise NotImplementedError("prediction_type not implemented yet: sample")
else:
raise ValueError(
f"prediction_type given as {scheduler.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
sigma_from = scheduler.sigmas[scheduler.step_index]
sigma_to = scheduler.sigmas[scheduler.step_index + 1]
sigma_up = (sigma_to**2 * (sigma_from**2 - sigma_to**2) / sigma_from**2) ** 0.5
sigma_down = (sigma_to**2 - sigma_up**2) ** 0.5
# 2. Convert to an ODE derivative
derivative = (sample - pred_original_sample) / sigma
dt = sigma_down - sigma
prev_sample = sample + derivative * dt
# Cast sample back to model compatible dtype
prev_sample = prev_sample.to(model_output.dtype)
# upon completion increase step index by one
scheduler._step_index += 1
return prev_sample
def deterministic_non_ancestral_euler_step(
model_output: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
sample: torch.FloatTensor,
eta: float = 0.0,
use_clipped_model_output: bool = False,
s_churn: float = 0.0,
s_tmin: float = 0.0,
s_tmax: float = float("inf"),
s_noise: float = 1.0,
generator: Optional[torch.Generator] = None,
variance_noise: Optional[torch.FloatTensor] = None,
return_dict: bool = True,
scheduler=None,
):
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
process from the learned model outputs (most often the predicted noise).
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
s_churn (`float`):
s_tmin (`float`):
s_tmax (`float`):
s_noise (`float`, defaults to 1.0):
Scaling factor for noise added to the sample.
generator (`torch.Generator`, *optional*):
A random number generator.
return_dict (`bool`):
Whether or not to return a [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or
tuple.
Returns:
[`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_euler_discrete.EulerDiscreteSchedulerOutput`] is
returned, otherwise a tuple is returned where the first element is the sample tensor.
"""
if (
isinstance(timestep, int)
or isinstance(timestep, torch.IntTensor)
or isinstance(timestep, torch.LongTensor)
):
raise ValueError(
(
"Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to"
" `EulerDiscreteScheduler.step()` is not supported. Make sure to pass"
" one of the `scheduler.timesteps` as a timestep."
),
)
if not scheduler.is_scale_input_called:
logger.warning(
"The `scale_model_input` function should be called before `step` to ensure correct denoising. "
"See `StableDiffusionPipeline` for a usage example."
)
if scheduler.step_index is None:
scheduler._init_step_index(timestep)
# Upcast to avoid precision issues when computing prev_sample
sample = sample.to(torch.float32)
sigma = scheduler.sigmas[scheduler.step_index]
gamma = (
min(s_churn / (len(scheduler.sigmas) - 1), 2**0.5 - 1)
if s_tmin <= sigma <= s_tmax
else 0.0
)
sigma_hat = sigma * (gamma + 1)
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
# NOTE: "original_sample" should not be an expected prediction_type but is left in for
# backwards compatibility
if (
scheduler.config.prediction_type == "original_sample"
or scheduler.config.prediction_type == "sample"
):
pred_original_sample = model_output
elif scheduler.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma_hat * model_output
elif scheduler.config.prediction_type == "v_prediction":
# denoised = model_output * c_out + input * c_skip
pred_original_sample = model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (
sample / (sigma**2 + 1)
)
else:
raise ValueError(
f"prediction_type given as {scheduler.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
# 2. Convert to an ODE derivative
derivative = (sample - pred_original_sample) / sigma_hat
dt = scheduler.sigmas[scheduler.step_index + 1] - sigma_hat
prev_sample = sample + derivative * dt
# Cast sample back to model compatible dtype
prev_sample = prev_sample.to(model_output.dtype)
# upon completion increase step index by one
scheduler._step_index += 1
return prev_sample
def deterministic_ddpm_step(
model_output: torch.FloatTensor,
timestep: Union[float, torch.FloatTensor],
sample: torch.FloatTensor,
eta,
use_clipped_model_output,
generator,
variance_noise,
return_dict,
scheduler,
):
"""
Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
process from the learned model outputs (most often the predicted noise).
Args:
model_output (`torch.FloatTensor`):
The direct output from learned diffusion model.
timestep (`float`):
The current discrete timestep in the diffusion chain.
sample (`torch.FloatTensor`):
A current instance of a sample created by the diffusion process.
generator (`torch.Generator`, *optional*):
A random number generator.
return_dict (`bool`, *optional*, defaults to `True`):
Whether or not to return a [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`.
Returns:
[`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] or `tuple`:
If return_dict is `True`, [`~schedulers.scheduling_ddpm.DDPMSchedulerOutput`] is returned, otherwise a
tuple is returned where the first element is the sample tensor.
"""
t = timestep
prev_t = scheduler.previous_timestep(t)
if model_output.shape[1] == sample.shape[1] * 2 and scheduler.variance_type in [
"learned",
"learned_range",
]:
model_output, predicted_variance = torch.split(
model_output, sample.shape[1], dim=1
)
else:
predicted_variance = None
# 1. compute alphas, betas
alpha_prod_t = scheduler.alphas_cumprod[t]
alpha_prod_t_prev = (
scheduler.alphas_cumprod[prev_t] if prev_t >= 0 else scheduler.one
)
beta_prod_t = 1 - alpha_prod_t
beta_prod_t_prev = 1 - alpha_prod_t_prev
current_alpha_t = alpha_prod_t / alpha_prod_t_prev
current_beta_t = 1 - current_alpha_t
# 2. compute predicted original sample from predicted noise also called
# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
if scheduler.config.prediction_type == "epsilon":
pred_original_sample = (
sample - beta_prod_t ** (0.5) * model_output
) / alpha_prod_t ** (0.5)
elif scheduler.config.prediction_type == "sample":
pred_original_sample = model_output
elif scheduler.config.prediction_type == "v_prediction":
pred_original_sample = (alpha_prod_t**0.5) * sample - (
beta_prod_t**0.5
) * model_output
else:
raise ValueError(
f"prediction_type given as {scheduler.config.prediction_type} must be one of `epsilon`, `sample` or"
" `v_prediction` for the DDPMScheduler."
)
# 3. Clip or threshold "predicted x_0"
if scheduler.config.thresholding:
pred_original_sample = scheduler._threshold_sample(pred_original_sample)
elif scheduler.config.clip_sample:
pred_original_sample = pred_original_sample.clamp(
-scheduler.config.clip_sample_range, scheduler.config.clip_sample_range
)
# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
pred_original_sample_coeff = (
alpha_prod_t_prev ** (0.5) * current_beta_t
) / beta_prod_t
current_sample_coeff = current_alpha_t ** (0.5) * beta_prod_t_prev / beta_prod_t
# 5. Compute predicted previous sample µ_t
# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
pred_prev_sample = (
pred_original_sample_coeff * pred_original_sample
+ current_sample_coeff * sample
)
return pred_prev_sample