wan/utils/fm_solvers_unipc.py

import math
from typing import List, Optional, Tuple, Union
import numpy as np
import torch
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.schedulers.scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
from diffusers.utils import deprecate, is_scipy_available
if is_scipy_available():
    import scipy.stats

class FlowUniPCMultistepScheduler(SchedulerMixin, ConfigMixin):
    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
    order = 1

    @register_to_config
    def __init__(self, num_train_timesteps: int=1000, solver_order: int=2, prediction_type: str='flow_prediction', shift: Optional[float]=1.0, use_dynamic_shifting=False, thresholding: bool=False, dynamic_thresholding_ratio: float=0.995, sample_max_value: float=1.0, predict_x0: bool=True, solver_type: str='bh2', lower_order_final: bool=True, disable_corrector: List[int]=[], solver_p: SchedulerMixin=None, timestep_spacing: str='linspace', steps_offset: int=0, final_sigmas_type: Optional[str]='zero'):
        if solver_type not in ['bh1', 'bh2']:
            if solver_type in ['midpoint', 'heun', 'logrho']:
                self.register_to_config(solver_type='bh2')
            else:
                raise NotImplementedError(f'{solver_type} is not implemented for {self.__class__}')
        self.predict_x0 = predict_x0
        self.num_inference_steps = None
        alphas = np.linspace(1, 1 / num_train_timesteps, num_train_timesteps)[::-1].copy()
        sigmas = 1.0 - alphas
        sigmas = torch.from_numpy(sigmas).to(dtype=torch.float32)
        if not use_dynamic_shifting:
            sigmas = shift * sigmas / (1 + (shift - 1) * sigmas)
        self.sigmas = sigmas
        self.timesteps = sigmas * num_train_timesteps
        self.model_outputs = [None] * solver_order
        self.timestep_list = [None] * solver_order
        self.lower_order_nums = 0
        self.disable_corrector = disable_corrector
        self.solver_p = solver_p
        self.last_sample = None
        self._step_index = None
        self._begin_index = None
        self.sigmas = self.sigmas.to('cpu')
        self.sigma_min = self.sigmas[-1].item()
        self.sigma_max = self.sigmas[0].item()

    @property
    def step_index(self):
        return self._step_index

    @property
    def begin_index(self):
        return self._begin_index

    def set_begin_index(self, begin_index: int=0):
        self._begin_index = begin_index

    def set_timesteps(self, num_inference_steps: Union[int, None]=None, device: Union[str, torch.device]=None, sigmas: Optional[List[float]]=None, mu: Optional[Union[float, None]]=None, shift: Optional[Union[float, None]]=None):
        if self.config.use_dynamic_shifting and mu is None:
            raise ValueError(' you have to pass a value for `mu` when `use_dynamic_shifting` is set to be `True`')
        if sigmas is None:
            sigmas = np.linspace(self.sigma_max, self.sigma_min, num_inference_steps + 1).copy()[:-1]
        if self.config.use_dynamic_shifting:
            sigmas = self.time_shift(mu, 1.0, sigmas)
        else:
            if shift is None:
                shift = self.config.shift
            sigmas = shift * sigmas / (1 + (shift - 1) * sigmas)
        if self.config.final_sigmas_type == 'sigma_min':
            sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
        elif self.config.final_sigmas_type == 'zero':
            sigma_last = 0
        else:
            raise ValueError(f"`final_sigmas_type` must be one of 'zero', or 'sigma_min', but got {self.config.final_sigmas_type}")
        timesteps = sigmas * self.config.num_train_timesteps
        sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
        self.sigmas = torch.from_numpy(sigmas)
        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
        self.num_inference_steps = len(timesteps)
        self.model_outputs = [None] * self.config.solver_order
        self.lower_order_nums = 0
        self.last_sample = None
        if self.solver_p:
            self.solver_p.set_timesteps(self.num_inference_steps, device=device)
        self._step_index = None
        self._begin_index = None
        self.sigmas = self.sigmas.to('cpu')

    def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
        dtype = sample.dtype
        batch_size, channels, *remaining_dims = sample.shape
        if dtype not in (torch.float32, torch.float64):
            sample = sample.float()
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))
        abs_sample = sample.abs()
        s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
        s = torch.clamp(s, min=1, max=self.config.sample_max_value)
        s = s.unsqueeze(1)
        sample = torch.clamp(sample, -s, s) / s
        sample = sample.reshape(batch_size, channels, *remaining_dims)
        sample = sample.to(dtype)
        return sample

    def _sigma_to_t(self, sigma):
        return sigma * self.config.num_train_timesteps

    def _sigma_to_alpha_sigma_t(self, sigma):
        return (1 - sigma, sigma)

    def time_shift(self, mu: float, sigma: float, t: torch.Tensor):
        return math.exp(mu) / (math.exp(mu) + (1 / t - 1) ** sigma)

    def convert_model_output(self, model_output: torch.Tensor, *args, sample: torch.Tensor=None, **kwargs) -> torch.Tensor:
        timestep = args[0] if len(args) > 0 else kwargs.pop('timestep', None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError('missing `sample` as a required keyward argument')
        if timestep is not None:
            deprecate('timesteps', '1.0.0', 'Passing `timesteps` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`')
        sigma = self.sigmas[self.step_index]
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        if self.predict_x0:
            if self.config.prediction_type == 'flow_prediction':
                sigma_t = self.sigmas[self.step_index]
                x0_pred = sample - sigma_t * model_output
            else:
                raise ValueError(f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, `v_prediction` or `flow_prediction` for the UniPCMultistepScheduler.')
            if self.config.thresholding:
                x0_pred = self._threshold_sample(x0_pred)
            return x0_pred
        else:
            if self.config.prediction_type == 'flow_prediction':
                sigma_t = self.sigmas[self.step_index]
                epsilon = sample - (1 - sigma_t) * model_output
            else:
                raise ValueError(f'prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, `v_prediction` or `flow_prediction` for the UniPCMultistepScheduler.')
            if self.config.thresholding:
                sigma_t = self.sigmas[self.step_index]
                x0_pred = sample - sigma_t * model_output
                x0_pred = self._threshold_sample(x0_pred)
                epsilon = model_output + x0_pred
            return epsilon

    def multistep_uni_p_bh_update(self, model_output: torch.Tensor, *args, sample: torch.Tensor=None, order: int=None, **kwargs) -> torch.Tensor:
        prev_timestep = args[0] if len(args) > 0 else kwargs.pop('prev_timestep', None)
        if sample is None:
            if len(args) > 1:
                sample = args[1]
            else:
                raise ValueError(' missing `sample` as a required keyward argument')
        if order is None:
            if len(args) > 2:
                order = args[2]
            else:
                raise ValueError(' missing `order` as a required keyward argument')
        if prev_timestep is not None:
            deprecate('prev_timestep', '1.0.0', 'Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`')
        model_output_list = self.model_outputs
        s0 = self.timestep_list[-1]
        m0 = model_output_list[-1]
        x = sample
        if self.solver_p:
            x_t = self.solver_p.step(model_output, s0, x).prev_sample
            return x_t
        sigma_t, sigma_s0 = (self.sigmas[self.step_index + 1], self.sigmas[self.step_index])
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
        h = lambda_t - lambda_s0
        device = sample.device
        rks = []
        D1s = []
        for i in range(1, order):
            si = self.step_index - i
            mi = model_output_list[-(i + 1)]
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk)
            D1s.append((mi - m0) / rk)
        rks.append(1.0)
        rks = torch.tensor(rks, device=device)
        R = []
        b = []
        hh = -h if self.predict_x0 else h
        h_phi_1 = torch.expm1(hh)
        h_phi_k = h_phi_1 / hh - 1
        factorial_i = 1
        if self.config.solver_type == 'bh1':
            B_h = hh
        elif self.config.solver_type == '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=device)
        if len(D1s) > 0:
            D1s = torch.stack(D1s, dim=1)
            if order == 2:
                rhos_p = torch.tensor([0.5], dtype=x.dtype, device=device)
            else:
                rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1]).to(device).to(x.dtype)
        else:
            D1s = None
        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
                pred_res = torch.einsum('k,bkc...->bc...', rhos_p, D1s)
            else:
                pred_res = 0
            x_t = x_t_ - alpha_t * B_h * pred_res
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
                pred_res = torch.einsum('k,bkc...->bc...', rhos_p, D1s)
            else:
                pred_res = 0
            x_t = x_t_ - sigma_t * B_h * pred_res
        x_t = x_t.to(x.dtype)
        return x_t

    def multistep_uni_c_bh_update(self, this_model_output: torch.Tensor, *args, last_sample: torch.Tensor=None, this_sample: torch.Tensor=None, order: int=None, **kwargs) -> torch.Tensor:
        this_timestep = args[0] if len(args) > 0 else kwargs.pop('this_timestep', None)
        if last_sample is None:
            if len(args) > 1:
                last_sample = args[1]
            else:
                raise ValueError(' missing`last_sample` as a required keyward argument')
        if this_sample is None:
            if len(args) > 2:
                this_sample = args[2]
            else:
                raise ValueError(' missing`this_sample` as a required keyward argument')
        if order is None:
            if len(args) > 3:
                order = args[3]
            else:
                raise ValueError(' missing`order` as a required keyward argument')
        if this_timestep is not None:
            deprecate('this_timestep', '1.0.0', 'Passing `this_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`')
        model_output_list = self.model_outputs
        m0 = model_output_list[-1]
        x = last_sample
        x_t = this_sample
        model_t = this_model_output
        sigma_t, sigma_s0 = (self.sigmas[self.step_index], self.sigmas[self.step_index - 1])
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
        alpha_s0, sigma_s0 = self._sigma_to_alpha_sigma_t(sigma_s0)
        lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
        lambda_s0 = torch.log(alpha_s0) - torch.log(sigma_s0)
        h = lambda_t - lambda_s0
        device = this_sample.device
        rks = []
        D1s = []
        for i in range(1, order):
            si = self.step_index - (i + 1)
            mi = model_output_list[-(i + 1)]
            alpha_si, sigma_si = self._sigma_to_alpha_sigma_t(self.sigmas[si])
            lambda_si = torch.log(alpha_si) - torch.log(sigma_si)
            rk = (lambda_si - lambda_s0) / h
            rks.append(rk)
            D1s.append((mi - m0) / rk)
        rks.append(1.0)
        rks = torch.tensor(rks, device=device)
        R = []
        b = []
        hh = -h if self.predict_x0 else h
        h_phi_1 = torch.expm1(hh)
        h_phi_k = h_phi_1 / hh - 1
        factorial_i = 1
        if self.config.solver_type == 'bh1':
            B_h = hh
        elif self.config.solver_type == '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=device)
        if len(D1s) > 0:
            D1s = torch.stack(D1s, dim=1)
        else:
            D1s = None
        if order == 1:
            rhos_c = torch.tensor([0.5], dtype=x.dtype, device=device)
        else:
            rhos_c = torch.linalg.solve(R, b).to(device).to(x.dtype)
        if self.predict_x0:
            x_t_ = sigma_t / sigma_s0 * x - alpha_t * h_phi_1 * m0
            if D1s is not None:
                corr_res = torch.einsum('k,bkc...->bc...', rhos_c[:-1], D1s)
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - alpha_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        else:
            x_t_ = alpha_t / alpha_s0 * x - sigma_t * h_phi_1 * m0
            if D1s is not None:
                corr_res = torch.einsum('k,bkc...->bc...', rhos_c[:-1], D1s)
            else:
                corr_res = 0
            D1_t = model_t - m0
            x_t = x_t_ - sigma_t * B_h * (corr_res + rhos_c[-1] * D1_t)
        x_t = x_t.to(x.dtype)
        return x_t

    def index_for_timestep(self, timestep, schedule_timesteps=None):
        if schedule_timesteps is None:
            schedule_timesteps = self.timesteps
        indices = (schedule_timesteps == timestep).nonzero()
        pos = 1 if len(indices) > 1 else 0
        return indices[pos].item()

    def _init_step_index(self, timestep):
        if self.begin_index is None:
            if isinstance(timestep, torch.Tensor):
                timestep = timestep.to(self.timesteps.device)
            self._step_index = self.index_for_timestep(timestep)
        else:
            self._step_index = self._begin_index

    def step(self, model_output: torch.Tensor, timestep: Union[int, torch.Tensor], sample: torch.Tensor, return_dict: bool=True, generator=None) -> Union[SchedulerOutput, Tuple]:
        if self.num_inference_steps is None:
            raise ValueError("Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler")
        if self.step_index is None:
            self._init_step_index(timestep)
        use_corrector = self.step_index > 0 and self.step_index - 1 not in self.disable_corrector and (self.last_sample is not None)
        model_output_convert = self.convert_model_output(model_output, sample=sample)
        if use_corrector:
            sample = self.multistep_uni_c_bh_update(this_model_output=model_output_convert, last_sample=self.last_sample, this_sample=sample, order=self.this_order)
        for i in range(self.config.solver_order - 1):
            self.model_outputs[i] = self.model_outputs[i + 1]
            self.timestep_list[i] = self.timestep_list[i + 1]
        self.model_outputs[-1] = model_output_convert
        self.timestep_list[-1] = timestep
        if self.config.lower_order_final:
            this_order = min(self.config.solver_order, len(self.timesteps) - self.step_index)
        else:
            this_order = self.config.solver_order
        self.this_order = min(this_order, self.lower_order_nums + 1)
        assert self.this_order > 0
        self.last_sample = sample
        prev_sample = self.multistep_uni_p_bh_update(model_output=model_output, sample=sample, order=self.this_order)
        if self.lower_order_nums < self.config.solver_order:
            self.lower_order_nums += 1
        self._step_index += 1
        if not return_dict:
            return (prev_sample,)
        return SchedulerOutput(prev_sample=prev_sample)

    def scale_model_input(self, sample: torch.Tensor, *args, **kwargs) -> torch.Tensor:
        return sample

    def add_noise(self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor:
        sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
        if original_samples.device.type == 'mps' and torch.is_floating_point(timesteps):
            schedule_timesteps = self.timesteps.to(original_samples.device, dtype=torch.float32)
            timesteps = timesteps.to(original_samples.device, dtype=torch.float32)
        else:
            schedule_timesteps = self.timesteps.to(original_samples.device)
            timesteps = timesteps.to(original_samples.device)
        if self.begin_index is None:
            step_indices = [self.index_for_timestep(t, schedule_timesteps) for t in timesteps]
        elif self.step_index is not None:
            step_indices = [self.step_index] * timesteps.shape[0]
        else:
            step_indices = [self.begin_index] * timesteps.shape[0]
        sigma = sigmas[step_indices].flatten()
        while len(sigma.shape) < len(original_samples.shape):
            sigma = sigma.unsqueeze(-1)
        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
        noisy_samples = alpha_t * original_samples + sigma_t * noise
        return noisy_samples

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