File size: 8,064 Bytes
d77a781
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
# Copyright 2022 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 typing import Optional, Tuple, Union

import numpy as np
import torch

from scipy import integrate

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput


class LMSDiscreteScheduler(SchedulerMixin, 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`.
    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
    [`~ConfigMixin.from_config`] functios.

    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 (`np.ndarray`, optional): TODO
            options to clip the variance used when adding noise to the denoised sample. Choose from `fixed_small`,
            `fixed_small_log`, `fixed_large`, `fixed_large_log`, `learned` or `learned_range`.
        timestep_values (`np.ndarry`, optional): TODO
        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.

    """

    @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[np.ndarray] = None,
        timestep_values: Optional[np.ndarray] = None,
        tensor_format: str = "pt",
    ):
        if trained_betas is not None:
            self.betas = np.asarray(trained_betas)
        if beta_schedule == "linear":
            self.betas = np.linspace(beta_start, beta_end, num_train_timesteps, dtype=np.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = np.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=np.float32) ** 2
        else:
            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = np.cumprod(self.alphas, axis=0)

        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5

        # setable values
        self.num_inference_steps = None
        self.timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
        self.derivatives = []

        self.tensor_format = tensor_format
        self.set_format(tensor_format=tensor_format)

    def get_lms_coefficient(self, 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 - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
            return prod

        integrated_coeff = integrate.quad(lms_derivative, self.sigmas[t], self.sigmas[t + 1], epsrel=1e-4)[0]

        return integrated_coeff

    def set_timesteps(self, num_inference_steps: int):
        """
        Sets the timesteps used for the diffusion chain. Supporting function to be run before inference.

        Args:
            num_inference_steps (`int`):
                the number of diffusion steps used when generating samples with a pre-trained model.
        """
        self.num_inference_steps = num_inference_steps
        self.timesteps = np.linspace(self.num_train_timesteps - 1, 0, num_inference_steps, dtype=float)

        low_idx = np.floor(self.timesteps).astype(int)
        high_idx = np.ceil(self.timesteps).astype(int)
        frac = np.mod(self.timesteps, 1.0)
        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
        sigmas = (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
        self.sigmas = np.concatenate([sigmas, [0.0]])

        self.derivatives = []

        self.set_format(tensor_format=self.tensor_format)

    def step(
        self,
        model_output: Union[torch.FloatTensor, np.ndarray],
        timestep: int,
        sample: Union[torch.FloatTensor, np.ndarray],
        order: int = 4,
        return_dict: bool = True,
    ) -> Union[SchedulerOutput, 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:
            model_output (`torch.FloatTensor` or `np.ndarray`): direct output from learned diffusion model.
            timestep (`int`): current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor` or `np.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 SchedulerOutput class

        Returns:
            [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
            [`~schedulers.scheduling_utils.SchedulerOutput`] if `return_dict` is True, otherwise a `tuple`. When
            returning a tuple, the first element is the sample tensor.

        """
        sigma = self.sigmas[timestep]

        # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
        pred_original_sample = sample - sigma * model_output

        # 2. Convert to an ODE derivative
        derivative = (sample - pred_original_sample) / sigma
        self.derivatives.append(derivative)
        if len(self.derivatives) > order:
            self.derivatives.pop(0)

        # 3. Compute linear multistep coefficients
        order = min(timestep + 1, order)
        lms_coeffs = [self.get_lms_coefficient(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(self.derivatives))
        )

        if not return_dict:
            return (prev_sample,)

        return SchedulerOutput(prev_sample=prev_sample)

    def add_noise(
        self,
        original_samples: Union[torch.FloatTensor, np.ndarray],
        noise: Union[torch.FloatTensor, np.ndarray],
        timesteps: Union[torch.IntTensor, np.ndarray],
    ) -> Union[torch.FloatTensor, np.ndarray]:
        sigmas = self.match_shape(self.sigmas[timesteps], noise)
        noisy_samples = original_samples + noise * sigmas

        return noisy_samples

    def __len__(self):
        return self.config.num_train_timesteps