File size: 11,077 Bytes
7f43c1b |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 |
# Copyright 2023 Katherine Crowson and The HuggingFace Team. All rights reserved.
#
# 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 dataclasses import dataclass
from typing import Optional, Tuple, Union
import flax
import jax.numpy as jnp
from scipy import integrate
from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils_flax import (
CommonSchedulerState,
FlaxKarrasDiffusionSchedulers,
FlaxSchedulerMixin,
FlaxSchedulerOutput,
broadcast_to_shape_from_left,
)
@flax.struct.dataclass
class LMSDiscreteSchedulerState:
common: CommonSchedulerState
# setable values
init_noise_sigma: jnp.ndarray
timesteps: jnp.ndarray
sigmas: jnp.ndarray
num_inference_steps: Optional[int] = None
# running values
derivatives: Optional[jnp.ndarray] = None
@classmethod
def create(
cls, common: CommonSchedulerState, init_noise_sigma: jnp.ndarray, timesteps: jnp.ndarray, sigmas: jnp.ndarray
):
return cls(common=common, init_noise_sigma=init_noise_sigma, timesteps=timesteps, sigmas=sigmas)
@dataclass
class FlaxLMSSchedulerOutput(FlaxSchedulerOutput):
state: LMSDiscreteSchedulerState
class FlaxLMSDiscreteScheduler(FlaxSchedulerMixin, ConfigMixin):
"""
Linear Multistep Scheduler for discrete beta schedules. Based on the original k-diffusion implementation by
Katherine Crowson:
https://github.com/crowsonkb/k-diffusion/blob/481677d114f6ea445aa009cf5bd7a9cdee909e47/k_diffusion/sampling.py#L181
[`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
[`SchedulerMixin`] provides general loading and saving functionality via the [`SchedulerMixin.save_pretrained`] and
[`~SchedulerMixin.from_pretrained`] functions.
Args:
num_train_timesteps (`int`): number of diffusion steps used to train the model.
beta_start (`float`): the starting `beta` value of inference.
beta_end (`float`): the final `beta` value.
beta_schedule (`str`):
the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
`linear` or `scaled_linear`.
trained_betas (`jnp.ndarray`, optional):
option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
prediction_type (`str`, default `epsilon`, optional):
prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
https://imagen.research.google/video/paper.pdf)
dtype (`jnp.dtype`, *optional*, defaults to `jnp.float32`):
the `dtype` used for params and computation.
"""
_compatibles = [e.name for e in FlaxKarrasDiffusionSchedulers]
dtype: jnp.dtype
@property
def has_state(self):
return True
@register_to_config
def __init__(
self,
num_train_timesteps: int = 1000,
beta_start: float = 0.0001,
beta_end: float = 0.02,
beta_schedule: str = "linear",
trained_betas: Optional[jnp.ndarray] = None,
prediction_type: str = "epsilon",
dtype: jnp.dtype = jnp.float32,
):
self.dtype = dtype
def create_state(self, common: Optional[CommonSchedulerState] = None) -> LMSDiscreteSchedulerState:
if common is None:
common = CommonSchedulerState.create(self)
timesteps = jnp.arange(0, self.config.num_train_timesteps).round()[::-1]
sigmas = ((1 - common.alphas_cumprod) / common.alphas_cumprod) ** 0.5
# standard deviation of the initial noise distribution
init_noise_sigma = sigmas.max()
return LMSDiscreteSchedulerState.create(
common=common,
init_noise_sigma=init_noise_sigma,
timesteps=timesteps,
sigmas=sigmas,
)
def scale_model_input(self, state: LMSDiscreteSchedulerState, sample: jnp.ndarray, timestep: int) -> jnp.ndarray:
"""
Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm.
Args:
state (`LMSDiscreteSchedulerState`):
the `FlaxLMSDiscreteScheduler` state data class instance.
sample (`jnp.ndarray`):
current instance of sample being created by diffusion process.
timestep (`int`):
current discrete timestep in the diffusion chain.
Returns:
`jnp.ndarray`: scaled input sample
"""
(step_index,) = jnp.where(state.timesteps == timestep, size=1)
step_index = step_index[0]
sigma = state.sigmas[step_index]
sample = sample / ((sigma**2 + 1) ** 0.5)
return sample
def get_lms_coefficient(self, state: LMSDiscreteSchedulerState, order, t, current_order):
"""
Compute a linear multistep coefficient.
Args:
order (TODO):
t (TODO):
current_order (TODO):
"""
def lms_derivative(tau):
prod = 1.0
for k in range(order):
if current_order == k:
continue
prod *= (tau - state.sigmas[t - k]) / (state.sigmas[t - current_order] - state.sigmas[t - k])
return prod
integrated_coeff = integrate.quad(lms_derivative, state.sigmas[t], state.sigmas[t + 1], epsrel=1e-4)[0]
return integrated_coeff
def set_timesteps(
self, state: LMSDiscreteSchedulerState, num_inference_steps: int, shape: Tuple = ()
) -> LMSDiscreteSchedulerState:
"""
Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.
Args:
state (`LMSDiscreteSchedulerState`):
the `FlaxLMSDiscreteScheduler` state data class instance.
num_inference_steps (`int`):
the number of diffusion steps used when generating samples with a pre-trained model.
"""
timesteps = jnp.linspace(self.config.num_train_timesteps - 1, 0, num_inference_steps, dtype=self.dtype)
low_idx = jnp.floor(timesteps).astype(jnp.int32)
high_idx = jnp.ceil(timesteps).astype(jnp.int32)
frac = jnp.mod(timesteps, 1.0)
sigmas = ((1 - state.common.alphas_cumprod) / state.common.alphas_cumprod) ** 0.5
sigmas = (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
sigmas = jnp.concatenate([sigmas, jnp.array([0.0], dtype=self.dtype)])
timesteps = timesteps.astype(jnp.int32)
# initial running values
derivatives = jnp.zeros((0,) + shape, dtype=self.dtype)
return state.replace(
timesteps=timesteps,
sigmas=sigmas,
num_inference_steps=num_inference_steps,
derivatives=derivatives,
)
def step(
self,
state: LMSDiscreteSchedulerState,
model_output: jnp.ndarray,
timestep: int,
sample: jnp.ndarray,
order: int = 4,
return_dict: bool = True,
) -> Union[FlaxLMSSchedulerOutput, Tuple]:
"""
Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
process from the learned model outputs (most often the predicted noise).
Args:
state (`LMSDiscreteSchedulerState`): the `FlaxLMSDiscreteScheduler` state data class instance.
model_output (`jnp.ndarray`): direct output from learned diffusion model.
timestep (`int`): current discrete timestep in the diffusion chain.
sample (`jnp.ndarray`):
current instance of sample being created by diffusion process.
order: coefficient for multi-step inference.
return_dict (`bool`): option for returning tuple rather than FlaxLMSSchedulerOutput class
Returns:
[`FlaxLMSSchedulerOutput`] or `tuple`: [`FlaxLMSSchedulerOutput`] if `return_dict` is True, otherwise a
`tuple`. When returning a tuple, the first element is the sample tensor.
"""
if state.num_inference_steps is None:
raise ValueError(
"Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
)
sigma = state.sigmas[timestep]
# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
if self.config.prediction_type == "epsilon":
pred_original_sample = sample - sigma * model_output
elif self.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))
else:
raise ValueError(
f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"
)
# 2. Convert to an ODE derivative
derivative = (sample - pred_original_sample) / sigma
state = state.replace(derivatives=jnp.append(state.derivatives, derivative))
if len(state.derivatives) > order:
state = state.replace(derivatives=jnp.delete(state.derivatives, 0))
# 3. Compute linear multistep coefficients
order = min(timestep + 1, order)
lms_coeffs = [self.get_lms_coefficient(state, order, timestep, curr_order) for curr_order in range(order)]
# 4. Compute previous sample based on the derivatives path
prev_sample = sample + sum(
coeff * derivative for coeff, derivative in zip(lms_coeffs, reversed(state.derivatives))
)
if not return_dict:
return (prev_sample, state)
return FlaxLMSSchedulerOutput(prev_sample=prev_sample, state=state)
def add_noise(
self,
state: LMSDiscreteSchedulerState,
original_samples: jnp.ndarray,
noise: jnp.ndarray,
timesteps: jnp.ndarray,
) -> jnp.ndarray:
sigma = state.sigmas[timesteps].flatten()
sigma = broadcast_to_shape_from_left(sigma, noise.shape)
noisy_samples = original_samples + noise * sigma
return noisy_samples
def __len__(self):
return self.config.num_train_timesteps
|