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 SchedulerMixin, SchedulerOutput class RungeKutta44Scheduler(SchedulerMixin, ConfigMixin): """ RK4: Classical 4th-order Runge-Kutta scheduler. Adapted from the RES4LYF repository. This scheduler uses 4 stages per step. """ order = 1 @register_to_config def __init__( self, num_train_timesteps: int = 1000, beta_start: float = 0.00085, beta_end: float = 0.012, beta_schedule: str = "linear", trained_betas: Optional[Union[np.ndarray, List[float]]] = None, prediction_type: str = "epsilon", use_karras_sigmas: bool = False, use_exponential_sigmas: bool = False, use_beta_sigmas: bool = False, use_flow_sigmas: bool = False, sigma_min: Optional[float] = None, sigma_max: Optional[float] = None, rho: float = 7.0, shift: Optional[float] = None, base_shift: float = 0.5, max_shift: float = 1.15, use_dynamic_shifting: bool = False, timestep_spacing: str = "linspace", clip_sample: bool = False, sample_max_value: float = 1.0, set_alpha_to_one: bool = False, skip_prk_steps: bool = False, interpolation_type: str = "linear", steps_offset: int = 0, timestep_type: str = "discrete", rescale_betas_zero_snr: bool = False, final_sigmas_type: str = "zero", ): if trained_betas is not None: self.betas = torch.tensor(trained_betas, dtype=torch.float32) elif beta_schedule == "linear": self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32) elif beta_schedule == "scaled_linear": self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2 else: raise NotImplementedError(f"{beta_schedule} is not implemented for RungeKutta44Scheduler") self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) self.sigmas = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy()) self.init_noise_sigma = 1.0 # Internal state for multi-stage self.model_outputs = [] self.sample_at_start_of_step = None self._sigmas_cpu = None self._step_index = None def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None, mu: Optional[float] = None, dtype: torch.dtype = torch.float32): self.num_inference_steps = num_inference_steps # 1. Base sigmas timesteps = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy() sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5) if self.config.interpolation_type == "linear": sigmas = np.interp(timesteps, np.arange(len(sigmas)), sigmas) elif self.config.interpolation_type == "log_linear": sigmas = np.exp(np.interp(timesteps, np.arange(len(sigmas)), np.log(sigmas))) else: raise ValueError(f"interpolation_type must be one of 'linear' or 'log_linear', got {self.config.interpolation_type}") if self.config.use_karras_sigmas: sigma_min = self.config.sigma_min if self.config.sigma_min is not None else sigmas[-1] sigma_max = self.config.sigma_max if self.config.sigma_max is not None else sigmas[0] rho = self.config.rho ramp = np.linspace(0, 1, num_inference_steps) min_inv_rho = sigma_min ** (1 / rho) max_inv_rho = sigma_max ** (1 / rho) sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho # 2. Add sub-step sigmas for multi-stage RK # RK4 has c = [0, 1/2, 1/2, 1] c_values = [0.0, 0.5, 0.5, 1.0] sigmas_expanded = [] for i in range(len(sigmas) - 1): s_curr = sigmas[i] s_next = sigmas[i + 1] # Intermediate sigmas: s_curr + c * (s_next - s_curr) for c in c_values: # Add a tiny epsilon to duplicate sigmas to allow distinct indexing if needed, # but better to rely on internal counter. sigmas_expanded.append(s_curr + c * (s_next - s_curr)) sigmas_expanded.append(0.0) # terminal sigma # 3. Map back to timesteps sigmas_interpolated = np.array(sigmas_expanded) # Linear remapping for Flow Matching timesteps_expanded = sigmas_interpolated * self.config.num_train_timesteps self.sigmas = torch.from_numpy(sigmas_interpolated).to(device=device, dtype=dtype) self.timesteps = torch.from_numpy(timesteps_expanded + self.config.steps_offset).to(device=device, dtype=dtype) self.init_noise_sigma = self.sigmas.max().item() if self.sigmas.numel() > 0 else 1.0 self._sigmas_cpu = self.sigmas.detach().cpu().numpy() self.model_outputs = [] self.sample_at_start_of_step = None self._step_index = None @property def step_index(self): """ The index counter for the current timestep. It will increase 1 after each scheduler step. """ return self._step_index def index_for_timestep(self, timestep, schedule_timesteps=None): if schedule_timesteps is None: schedule_timesteps = self.timesteps # Use argmin for robust float matching index = torch.abs(schedule_timesteps - timestep).argmin().item() return index def _init_step_index(self, timestep): if isinstance(timestep, torch.Tensor): timestep = timestep.to(self.timesteps.device) self._step_index = self.index_for_timestep(timestep) def scale_model_input(self, sample: torch.Tensor, timestep: Union[float, torch.Tensor]) -> torch.Tensor: if self._step_index is None: self._init_step_index(timestep) if self.config.prediction_type == "flow_prediction": return sample sigma = self._sigmas_cpu[self._step_index] return sample / ((sigma**2 + 1) ** 0.5) def step( self, model_output: torch.Tensor, timestep: Union[float, torch.Tensor], sample: torch.Tensor, return_dict: bool = True, ) -> Union[SchedulerOutput, Tuple]: if self._step_index is None: self._init_step_index(timestep) step_index = self._step_index stage_index = step_index % 4 # Current and next step interval sigmas base_step_index = (step_index // 4) * 4 sigma_curr = self._sigmas_cpu[base_step_index] sigma_next_idx = min(base_step_index + 4, len(self._sigmas_cpu) - 1) sigma_next = self._sigmas_cpu[sigma_next_idx] # The sigma at the end of this 4-stage step h = sigma_next - sigma_curr sigma_t = self._sigmas_cpu[step_index] alpha_t = 1 / (sigma_t**2 + 1) ** 0.5 sigma_actual = sigma_t * alpha_t prediction_type = getattr(self.config, "prediction_type", "epsilon") if prediction_type == "epsilon": denoised = sample - sigma_t * model_output elif prediction_type == "v_prediction": alpha_t = 1 / (sigma_t**2 + 1) ** 0.5 sigma_actual = sigma_t * alpha_t denoised = alpha_t * sample - sigma_actual * model_output elif prediction_type == "flow_prediction": denoised = sample - sigma_t * model_output elif prediction_type == "sample": denoised = model_output else: raise ValueError(f"prediction_type error: {prediction_type}") if self.config.clip_sample: denoised = denoised.clamp(-self.config.sample_max_value, self.config.sample_max_value) # derivative = (x - x0) / sigma derivative = (sample - denoised) / sigma_t if sigma_t > 1e-6 else torch.zeros_like(sample) if self.sample_at_start_of_step is None: if stage_index > 0: # Mid-step fallback for Img2Img/Inpainting sigma_next_t = self._sigmas_cpu[self._step_index + 1] dt = sigma_next_t - sigma_t prev_sample = sample + dt * derivative self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) self.sample_at_start_of_step = sample self.model_outputs = [derivative] * stage_index if stage_index == 0: self.model_outputs = [derivative] self.sample_at_start_of_step = sample # Stage 2 input: y + 0.5 * h * k1 prev_sample = self.sample_at_start_of_step + 0.5 * h * derivative elif stage_index == 1: self.model_outputs.append(derivative) # Stage 3 input: y + 0.5 * h * k2 prev_sample = self.sample_at_start_of_step + 0.5 * h * derivative elif stage_index == 2: self.model_outputs.append(derivative) # Stage 4 input: y + h * k3 prev_sample = self.sample_at_start_of_step + h * derivative elif stage_index == 3: self.model_outputs.append(derivative) # Final result: y + (h/6) * (k1 + 2*k2 + 2*k3 + k4) k1, k2, k3, k4 = self.model_outputs prev_sample = self.sample_at_start_of_step + (h / 6.0) * (k1 + 2 * k2 + 2 * k3 + k4) # Clear state self.model_outputs = [] self.sample_at_start_of_step = None # Increment step index self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) def add_noise( self, original_samples: torch.Tensor, noise: torch.Tensor, timesteps: torch.Tensor, ) -> torch.Tensor: from .scheduler_utils import add_noise_to_sample return add_noise_to_sample(original_samples, noise, self.sigmas, timesteps, self.timesteps) def __len__(self): return self.config.num_train_timesteps