import numpy as np import torch from diffusers.configuration_utils import ConfigMixin, register_to_config from diffusers.schedulers.scheduling_utils import SchedulerMixin, SchedulerOutput class GaussLegendreScheduler(SchedulerMixin, ConfigMixin): """ GaussLegendreScheduler: High-accuracy implicit symplectic integrators. Supports various orders (2s, 3s, 4s, 5s, 8s-diagonal). Adapted from the RES4LYF repository. """ 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: np.ndarray | list[float] | None = None, prediction_type: str = "epsilon", variant: str = "gauss-legendre_2s", # 2s to 8s variants use_karras_sigmas: bool = False, use_exponential_sigmas: bool = False, use_beta_sigmas: bool = False, use_flow_sigmas: bool = False, sigma_min: float | None = None, sigma_max: float | None = None, rho: float = 7.0, shift: float | None = 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") self.alphas = 1.0 - self.betas self.alphas_cumprod = torch.cumprod(self.alphas, dim=0) self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy()) self.sigmas = None self.init_noise_sigma = 1.0 # Internal state self.model_outputs = [] self.sample_at_start_of_step = None self._step_index = None def _get_tableau(self): v = self.config.variant if v == "gauss-legendre_2s": r3 = 3**0.5 a = [[1 / 4, 1 / 4 - r3 / 6], [1 / 4 + r3 / 6, 1 / 4]] b = [1 / 2, 1 / 2] c = [1 / 2 - r3 / 6, 1 / 2 + r3 / 6] elif v == "gauss-legendre_3s": r15 = 15**0.5 a = [[5 / 36, 2 / 9 - r15 / 15, 5 / 36 - r15 / 30], [5 / 36 + r15 / 24, 2 / 9, 5 / 36 - r15 / 24], [5 / 36 + r15 / 30, 2 / 9 + r15 / 15, 5 / 36]] b = [5 / 18, 4 / 9, 5 / 18] c = [1 / 2 - r15 / 10, 1 / 2, 1 / 2 + r15 / 10] elif v == "gauss-legendre_4s": r15 = 15**0.5 a = [[1 / 4, 1 / 4 - r15 / 6, 1 / 4 + r15 / 6, 1 / 4], [1 / 4 + r15 / 6, 1 / 4, 1 / 4 - r15 / 6, 1 / 4], [1 / 4, 1 / 4 + r15 / 6, 1 / 4, 1 / 4 - r15 / 6], [1 / 4 - r15 / 6, 1 / 4, 1 / 4 + r15 / 6, 1 / 4]] b = [1 / 8, 3 / 8, 3 / 8, 1 / 8] c = [1 / 2 - r15 / 10, 1 / 2 + r15 / 10, 1 / 2 + r15 / 10, 1 / 2 - r15 / 10] elif v == "gauss-legendre_5s": r739 = 739**0.5 a = [ [ 4563950663 / 32115191526, (310937500000000 / 2597974476091533 + 45156250000 * r739 / 8747388808389), (310937500000000 / 2597974476091533 - 45156250000 * r739 / 8747388808389), (5236016175 / 88357462711 + 709703235 * r739 / 353429850844), (5236016175 / 88357462711 - 709703235 * r739 / 353429850844), ], [ (4563950663 / 32115191526 - 38339103 * r739 / 6250000000), (310937500000000 / 2597974476091533 + 9557056475401 * r739 / 3498955523355600000), (310937500000000 / 2597974476091533 - 14074198220719489 * r739 / 3498955523355600000), (5236016175 / 88357462711 + 5601362553163918341 * r739 / 2208936567775000000000), (5236016175 / 88357462711 - 5040458465159165409 * r739 / 2208936567775000000000), ], [ (4563950663 / 32115191526 + 38339103 * r739 / 6250000000), (310937500000000 / 2597974476091533 + 14074198220719489 * r739 / 3498955523355600000), (310937500000000 / 2597974476091533 - 9557056475401 * r739 / 3498955523355600000), (5236016175 / 88357462711 + 5040458465159165409 * r739 / 2208936567775000000000), (5236016175 / 88357462711 - 5601362553163918341 * r739 / 2208936567775000000000), ], [ (4563950663 / 32115191526 - 38209 * r739 / 7938810), (310937500000000 / 2597974476091533 - 359369071093750 * r739 / 70145310854471391), (310937500000000 / 2597974476091533 - 323282178906250 * r739 / 70145310854471391), (5236016175 / 88357462711 - 470139 * r739 / 1413719403376), (5236016175 / 88357462711 - 44986764863 * r739 / 21205791050640), ], [ (4563950663 / 32115191526 + 38209 * r739 / 7938810), (310937500000000 / 2597974476091533 + 359369071093750 * r739 / 70145310854471391), (310937500000000 / 2597974476091533 + 323282178906250 * r739 / 70145310854471391), (5236016175 / 88357462711 + 44986764863 * r739 / 21205791050640), (5236016175 / 88357462711 + 470139 * r739 / 1413719403376), ], ] b = [4563950663 / 16057595763, 621875000000000 / 2597974476091533, 621875000000000 / 2597974476091533, 10472032350 / 88357462711, 10472032350 / 88357462711] c = [1 / 2, 1 / 2 - 99 * r739 / 10000, 1 / 2 + 99 * r739 / 10000, 1 / 2 - r739 / 60, 1 / 2 + r739 / 60] elif v == "gauss-legendre_diag_8s": a = [ [0.5, 0, 0, 0, 0, 0, 0, 0], [1.0818949631055815, 0.5, 0, 0, 0, 0, 0, 0], [0.9599572962220549, 1.0869589243008327, 0.5, 0, 0, 0, 0, 0], [1.0247213458032004, 0.9550588736973743, 1.0880938387323083, 0.5, 0, 0, 0, 0], [0.9830238267636289, 1.0287597754747493, 0.9538345351852, 1.0883471611098278, 0.5, 0, 0, 0], [1.0122259141132982, 0.9799828723635913, 1.0296038730649779, 0.9538345351852, 1.0880938387323083, 0.5, 0, 0], [0.9912514332308026, 1.0140743558891669, 0.9799828723635913, 1.0287597754747493, 0.9550588736973743, 1.0869589243008327, 0.5, 0], [1.0054828082532159, 0.9912514332308026, 1.0122259141132982, 0.9830238267636289, 1.0247213458032004, 0.9599572962220549, 1.0818949631055815, 0.5], ] b = [0.05061426814518813, 0.11119051722668724, 0.15685332293894364, 0.181341891689181, 0.181341891689181, 0.15685332293894364, 0.11119051722668724, 0.05061426814518813] c = [0.019855071751231884, 0.10166676129318663, 0.2372337950418355, 0.4082826787521751, 0.5917173212478249, 0.7627662049581645, 0.8983332387068134, 0.9801449282487681] else: raise ValueError(f"Unknown variant: {v}") return np.array(a), np.array(b), np.array(c) def set_timesteps( self, num_inference_steps: int, device: str | torch.device = None, mu: float | None = None, dtype: torch.dtype = torch.float32): self.num_inference_steps = num_inference_steps # 1. Spacing if self.config.timestep_spacing == "linspace": timesteps = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy() elif self.config.timestep_spacing == "leading": step_ratio = self.config.num_train_timesteps // num_inference_steps timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(float) elif self.config.timestep_spacing == "trailing": step_ratio = self.config.num_train_timesteps / num_inference_steps timesteps = (np.arange(self.config.num_train_timesteps, 0, -step_ratio)).round().copy().astype(float) timesteps -= 1 else: raise ValueError(f"timestep_spacing must be one of 'linspace', 'leading', or 'trailing', got {self.config.timestep_spacing}") 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}") # 2. Sigma Schedule 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) sigmas = (sigma_max ** (1 / rho) + ramp * (sigma_min ** (1 / rho) - sigma_max ** (1 / rho))) ** rho elif self.config.use_exponential_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] sigmas = np.exp(np.linspace(np.log(sigma_max), np.log(sigma_min), num_inference_steps)) elif self.config.use_beta_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] alpha, beta = 0.6, 0.6 ramp = np.linspace(0, 1, num_inference_steps) try: import torch.distributions as dist b = dist.Beta(alpha, beta) ramp = b.sample((num_inference_steps,)).sort().values.numpy() except Exception: pass sigmas = sigma_max * (1 - ramp) + sigma_min * ramp elif self.config.use_flow_sigmas: sigmas = np.linspace(1.0, 1 / 1000, num_inference_steps) # 3. Shifting if self.config.use_dynamic_shifting and mu is not None: sigmas = mu * sigmas / (1 + (mu - 1) * sigmas) elif self.config.shift is not None: sigmas = self.config.shift * sigmas / (1 + (self.config.shift - 1) * sigmas) # We handle multi-history expansion _a_mat, _b_vec, c_vec = self._get_tableau() len(c_vec) sigmas_expanded = [] for i in range(len(sigmas) - 1): s_curr = sigmas[i] s_next = sigmas[i + 1] for c_val in c_vec: sigmas_expanded.append(s_curr + c_val * (s_next - s_curr)) sigmas_expanded.append(0.0) 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.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): from .scheduler_utils import index_for_timestep if schedule_timesteps is None: schedule_timesteps = self.timesteps return index_for_timestep(timestep, schedule_timesteps) def _init_step_index(self, timestep): if self._step_index is None: 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: 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[self._step_index] return sample / ((sigma**2 + 1) ** 0.5) def step( self, model_output: torch.Tensor, timestep: float | torch.Tensor, sample: torch.Tensor, return_dict: bool = True, ) -> SchedulerOutput | tuple: if self._step_index is None: self._init_step_index(timestep) step_index = self._step_index a_mat, b_vec, c_vec = self._get_tableau() num_stages = len(c_vec) stage_index = step_index % num_stages base_step_index = (step_index // num_stages) * num_stages sigma_curr = self.sigmas[base_step_index] sigma_next_idx = min(base_step_index + num_stages, len(self.sigmas) - 1) sigma_next = self.sigmas[sigma_next_idx] if sigma_next <= 0: sigma_t = self.sigmas[step_index] 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 else: denoised = model_output if getattr(self.config, "clip_sample", False): denoised = denoised.clamp(-self.config.sample_max_value, self.config.sample_max_value) prev_sample = denoised self._step_index += 1 if not return_dict: return (prev_sample,) return SchedulerOutput(prev_sample=prev_sample) h = sigma_next - sigma_curr sigma_t = self.sigmas[step_index] prediction_type = getattr(self.config, "prediction_type", "epsilon") if prediction_type == "epsilon": denoised = sample - sigma_t * model_output elif self.config.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[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 else: self.model_outputs.append(derivative) # Predict sample for next stage next_stage_idx = stage_index + 1 if next_stage_idx < num_stages: sum_ak = 0 for j in range(len(self.model_outputs)): sum_ak = sum_ak + a_mat[next_stage_idx][j] * self.model_outputs[j] sigma_next_stage = self.sigmas[min(step_index + 1, len(self.sigmas) - 1)] # Update x (unnormalized sample) prev_sample = self.sample_at_start_of_step + (sigma_next_stage - sigma_curr) * sum_ak else: # Final step update using b coefficients sum_bk = 0 for j in range(len(self.model_outputs)): sum_bk = sum_bk + b_vec[j] * self.model_outputs[j] prev_sample = self.sample_at_start_of_step + h * sum_bk self.model_outputs = [] self.sample_at_start_of_step = None 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