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# Copyright (c) 2024 Bytedance Ltd. and/or its affiliates
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from .base import *
class DPMSolverSingleStepScheduler(Scheduler):
def __init__(
self,
# Generic scheduler settings
num_train_timesteps: int,
num_inference_timesteps: int,
betas: torch.Tensor,
inference_timesteps: Union[str, List[int]] = "trailing",
set_alpha_to_one: bool = True,
device: Optional[Union[str, torch.device]] = None,
dtype: torch.dtype = torch.float32,
# DPM scheduler settings
algorithm_type: str = "dpmsolver++",
solver_type: str = "midpoint",
solver_order: int = 2,
lower_order_final: bool = True,
):
super().__init__(
num_train_timesteps=num_train_timesteps,
num_inference_timesteps=num_inference_timesteps,
betas=betas,
inference_timesteps=inference_timesteps,
set_alpha_to_one=set_alpha_to_one,
device=device,
dtype=dtype,
)
self.solver_order = solver_order
self.solver_type = solver_type
self.lower_order_final = lower_order_final
self.algorithm_type = algorithm_type
self.alpha_t = torch.sqrt(self.alphas_cumprod)
self.sigma_t = torch.sqrt(1 - self.alphas_cumprod)
self.lambda_t = torch.log(self.alpha_t) - torch.log(self.sigma_t)
self.reset()
def reset(self):
self.model_outputs = [None] * self.solver_order
self.sample = None
self.order_list = self.get_order_list()
self.last_step_index = None
def get_order_list(self) -> List[int]:
steps = self.num_inference_timesteps
order = self.solver_order
# First step must be order 1
# Second step must be order 1 in case of terminal zero SNR
orders = [1] + [(i % order) + 1 for i in range(steps - 1)] + [1]
# Last step should be order 1 for better quality.
if self.lower_order_final:
orders[-1] = 1
return orders
def dpm_solver_first_order_update(
self,
model_output: torch.FloatTensor,
timestep: int,
prev_timestep: int,
sample: torch.FloatTensor,
) -> torch.FloatTensor:
lambda_t, lambda_s = self.lambda_t[prev_timestep], self.lambda_t[timestep]
alpha_t, alpha_s = self.alpha_t[prev_timestep], self.alpha_t[timestep]
sigma_t, sigma_s = self.sigma_t[prev_timestep], self.sigma_t[timestep]
h = lambda_t - lambda_s
if self.algorithm_type == "dpmsolver++":
x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output
elif self.algorithm_type == "dpmsolver":
x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
return x_t
def singlestep_dpm_solver_second_order_update(
self,
model_output_list: List[torch.FloatTensor],
timestep_list: List[int],
prev_timestep: int,
sample: torch.FloatTensor,
) -> torch.FloatTensor:
t, s0, s1 = prev_timestep, timestep_list[-1], timestep_list[-2]
m0, m1 = model_output_list[-1], model_output_list[-2]
lambda_t, lambda_s0, lambda_s1 = self.lambda_t[t], self.lambda_t[s0], self.lambda_t[s1]
alpha_t, alpha_s1 = self.alpha_t[t], self.alpha_t[s1]
sigma_t, sigma_s1 = self.sigma_t[t], self.sigma_t[s1]
h, h_0 = lambda_t - lambda_s1, lambda_s0 - lambda_s1
r0 = h_0 / h
D0, D1 = m1, (1.0 / r0) * (m0 - m1)
if self.algorithm_type == "dpmsolver++":
# See https://arxiv.org/abs/2211.01095 for detailed derivations
if self.solver_type == "midpoint":
x_t = (
(sigma_t / sigma_s1) * sample
- (alpha_t * (torch.exp(-h) - 1.0)) * D0
- 0.5 * (alpha_t * (torch.exp(-h) - 1.0)) * D1
)
elif self.solver_type == "heun":
x_t = (
(sigma_t / sigma_s1) * sample
- (alpha_t * (torch.exp(-h) - 1.0)) * D0
+ (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
)
elif self.algorithm_type == "dpmsolver":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
if self.solver_type == "midpoint":
x_t = (
(alpha_t / alpha_s1) * sample
- (sigma_t * (torch.exp(h) - 1.0)) * D0
- 0.5 * (sigma_t * (torch.exp(h) - 1.0)) * D1
)
elif self.solver_type == "heun":
x_t = (
(alpha_t / alpha_s1) * sample
- (sigma_t * (torch.exp(h) - 1.0)) * D0
- (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
)
return x_t
def singlestep_dpm_solver_third_order_update(
self,
model_output_list: List[torch.FloatTensor],
timestep_list: List[int],
prev_timestep: int,
sample: torch.FloatTensor,
) -> torch.FloatTensor:
t, s0, s1, s2 = prev_timestep, timestep_list[-1], timestep_list[-2], timestep_list[-3]
m0, m1, m2 = model_output_list[-1], model_output_list[-2], model_output_list[-3]
lambda_t, lambda_s0, lambda_s1, lambda_s2 = (
self.lambda_t[t],
self.lambda_t[s0],
self.lambda_t[s1],
self.lambda_t[s2],
)
alpha_t, alpha_s2 = self.alpha_t[t], self.alpha_t[s2]
sigma_t, sigma_s2 = self.sigma_t[t], self.sigma_t[s2]
h, h_0, h_1 = lambda_t - lambda_s2, lambda_s0 - lambda_s2, lambda_s1 - lambda_s2
r0, r1 = h_0 / h, h_1 / h
D0 = m2
D1_0, D1_1 = (1.0 / r1) * (m1 - m2), (1.0 / r0) * (m0 - m2)
D1 = (r0 * D1_0 - r1 * D1_1) / (r0 - r1)
D2 = 2.0 * (D1_1 - D1_0) / (r0 - r1)
if self.algorithm_type == "dpmsolver++":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
if self.solver_type == "midpoint":
x_t = (
(sigma_t / sigma_s2) * sample
- (alpha_t * (torch.exp(-h) - 1.0)) * D0
+ (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1_1
)
elif self.solver_type == "heun":
x_t = (
(sigma_t / sigma_s2) * sample
- (alpha_t * (torch.exp(-h) - 1.0)) * D0
+ (alpha_t * ((torch.exp(-h) - 1.0) / h + 1.0)) * D1
- (alpha_t * ((torch.exp(-h) - 1.0 + h) / h**2 - 0.5)) * D2
)
elif self.algorithm_type == "dpmsolver":
# See https://arxiv.org/abs/2206.00927 for detailed derivations
if self.solver_type == "midpoint":
x_t = (
(alpha_t / alpha_s2) * sample
- (sigma_t * (torch.exp(h) - 1.0)) * D0
- (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1_1
)
elif self.solver_type == "heun":
x_t = (
(alpha_t / alpha_s2) * sample
- (sigma_t * (torch.exp(h) - 1.0)) * D0
- (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
- (sigma_t * ((torch.exp(h) - 1.0 - h) / h**2 - 0.5)) * D2
)
return x_t
def step(
self,
model_output: torch.FloatTensor,
model_output_type: str,
timestep: int,
sample: torch.FloatTensor,
) -> SchedulerStepOutput:
step_index = (self.timesteps == timestep).nonzero().item()
# Check if this step is the follow-up of the previous step.
# If not, then we reset and treat it as a new run.
if self.last_step_index and self.last_step_index != step_index - 1:
self.reset()
self.last_step_index = step_index
prev_timestep = 0 if step_index == len(self.timesteps) - 1 else self.timesteps[step_index + 1]
model_output_convert = self.convert_output(model_output, model_output_type, sample, timestep)
if self.algorithm_type == "dpmsolver++":
model_output = model_output_convert.pred_original_sample
else:
model_output = model_output_convert.pred_epsilon
for i in range(self.solver_order - 1):
self.model_outputs[i] = self.model_outputs[i + 1]
self.model_outputs[-1] = model_output
order = self.order_list[step_index]
# For img2img denoising might start with order>1 which is not possible
# In this case make sure that the first two steps are both order=1
while self.model_outputs[-order] is None:
order -= 1
# For single-step solvers, we use the initial value at each time with order = 1.
if order == 1:
self.sample = sample
timestep_list = [self.timesteps[step_index - i] for i in range(order - 1, 0, -1)] + [timestep]
if order == 1:
prev_sample = self.dpm_solver_first_order_update(self.model_outputs[-1], timestep_list[-1], prev_timestep, self.sample)
elif order == 2:
prev_sample = self.singlestep_dpm_solver_second_order_update(self.model_outputs, timestep_list, prev_timestep, self.sample)
elif order == 3:
prev_sample = self.singlestep_dpm_solver_third_order_update(self.model_outputs, timestep_list, prev_timestep, self.sample)
else:
raise NotImplementedError
return SchedulerStepOutput(
prev_sample=prev_sample,
pred_original_sample=model_output_convert.pred_original_sample
)
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