diff --git a/comfy/k_diffusion/sa_solver.py b/comfy/k_diffusion/sa_solver.py new file mode 100644 index 000000000..af3e4c7b2 --- /dev/null +++ b/comfy/k_diffusion/sa_solver.py @@ -0,0 +1,198 @@ +# Modify from: https://github.com/scxue/SA-Solver +# MIT license +from typing import Union, Callable +import torch + + +def get_coefficients_exponential_positive(order, interval_start, interval_end, tau): + """ + Calculate the integral of exp(x(1+tau^2)) * x^order dx from interval_start to interval_end + For calculating the coefficient of gradient terms after the lagrange interpolation, + see Eq.(15) and Eq.(18) in SA-Solver paper https://arxiv.org/pdf/2309.05019.pdf + For data_prediction formula. + """ + assert order in [0, 1, 2, 3], "order is only supported for 0, 1, 2 and 3" + + # after change of variable(cov) + interval_end_cov = (1 + tau ** 2) * interval_end + interval_start_cov = (1 + tau ** 2) * interval_start + + if order == 0: + return (torch.exp(interval_end_cov) + * (1 - torch.exp(-(interval_end_cov - interval_start_cov))) + / ((1 + tau ** 2)) + ) + elif order == 1: + return (torch.exp(interval_end_cov) + * ((interval_end_cov - 1) - (interval_start_cov - 1) * torch.exp(-(interval_end_cov - interval_start_cov))) + / ((1 + tau ** 2) ** 2) + ) + elif order == 2: + return (torch.exp(interval_end_cov) + * ((interval_end_cov ** 2 - 2 * interval_end_cov + 2) + - (interval_start_cov ** 2 - 2 * interval_start_cov + 2) + * torch.exp(-(interval_end_cov - interval_start_cov)) + ) + / ((1 + tau ** 2) ** 3) + ) + elif order == 3: + return (torch.exp(interval_end_cov) + * ((interval_end_cov ** 3 - 3 * interval_end_cov ** 2 + 6 * interval_end_cov - 6) + - (interval_start_cov ** 3 - 3 * interval_start_cov ** 2 + 6 * interval_start_cov - 6) + * torch.exp(-(interval_end_cov - interval_start_cov)) + ) + / ((1 + tau ** 2) ** 4) + ) + + +def lagrange_polynomial_coefficient(order, lambda_list): + """ + Calculate the coefficient of lagrange polynomial + For lagrange interpolation + """ + assert order in [0, 1, 2, 3] + assert order == len(lambda_list) - 1 + if order == 0: + return [[1.0]] + elif order == 1: + return [[1.0 / (lambda_list[0] - lambda_list[1]), -lambda_list[1] / (lambda_list[0] - lambda_list[1])], + [1.0 / (lambda_list[1] - lambda_list[0]), -lambda_list[0] / (lambda_list[1] - lambda_list[0])]] + elif order == 2: + denominator1 = (lambda_list[0] - lambda_list[1]) * (lambda_list[0] - lambda_list[2]) + denominator2 = (lambda_list[1] - lambda_list[0]) * (lambda_list[1] - lambda_list[2]) + denominator3 = (lambda_list[2] - lambda_list[0]) * (lambda_list[2] - lambda_list[1]) + return [[1.0 / denominator1, (-lambda_list[1] - lambda_list[2]) / denominator1, lambda_list[1] * lambda_list[2] / denominator1], + [1.0 / denominator2, (-lambda_list[0] - lambda_list[2]) / denominator2, lambda_list[0] * lambda_list[2] / denominator2], + [1.0 / denominator3, (-lambda_list[0] - lambda_list[1]) / denominator3, lambda_list[0] * lambda_list[1] / denominator3] + ] + elif order == 3: + denominator1 = (lambda_list[0] - lambda_list[1]) * (lambda_list[0] - lambda_list[2]) * (lambda_list[0] - lambda_list[3]) + denominator2 = (lambda_list[1] - lambda_list[0]) * (lambda_list[1] - lambda_list[2]) * (lambda_list[1] - lambda_list[3]) + denominator3 = (lambda_list[2] - lambda_list[0]) * (lambda_list[2] - lambda_list[1]) * (lambda_list[2] - lambda_list[3]) + denominator4 = (lambda_list[3] - lambda_list[0]) * (lambda_list[3] - lambda_list[1]) * (lambda_list[3] - lambda_list[2]) + return [[1.0 / denominator1, + (-lambda_list[1] - lambda_list[2] - lambda_list[3]) / denominator1, + (lambda_list[1] * lambda_list[2] + lambda_list[1] * lambda_list[3] + lambda_list[2] * lambda_list[3]) / denominator1, + (-lambda_list[1] * lambda_list[2] * lambda_list[3]) / denominator1], + + [1.0 / denominator2, + (-lambda_list[0] - lambda_list[2] - lambda_list[3]) / denominator2, + (lambda_list[0] * lambda_list[2] + lambda_list[0] * lambda_list[3] + lambda_list[2] * lambda_list[3]) / denominator2, + (-lambda_list[0] * lambda_list[2] * lambda_list[3]) / denominator2], + + [1.0 / denominator3, + (-lambda_list[0] - lambda_list[1] - lambda_list[3]) / denominator3, + (lambda_list[0] * lambda_list[1] + lambda_list[0] * lambda_list[3] + lambda_list[1] * lambda_list[3]) / denominator3, + (-lambda_list[0] * lambda_list[1] * lambda_list[3]) / denominator3], + + [1.0 / denominator4, + (-lambda_list[0] - lambda_list[1] - lambda_list[2]) / denominator4, + (lambda_list[0] * lambda_list[1] + lambda_list[0] * lambda_list[2] + lambda_list[1] * lambda_list[2]) / denominator4, + (-lambda_list[0] * lambda_list[1] * lambda_list[2]) / denominator4] + ] + + +def get_coefficients_fn(order, interval_start, interval_end, lambda_list, tau): + """ + Calculate the coefficient of gradients. + """ + assert order in [1, 2, 3, 4] + assert order == len(lambda_list), 'the length of lambda list must be equal to the order' + lagrange_coefficient = lagrange_polynomial_coefficient(order - 1, lambda_list) + coefficients = [sum(lagrange_coefficient[i][j] * get_coefficients_exponential_positive(order - 1 - j, interval_start, interval_end, tau) + for j in range(order)) + for i in range(order)] + assert len(coefficients) == order, 'the length of coefficients does not match the order' + return coefficients + + +def adams_bashforth_update_few_steps(order, x, tau, model_prev_list, sigma_prev_list, noise, sigma): + """ + SA-Predictor, with the "rescaling" trick in Appendix D in SA-Solver paper https://arxiv.org/pdf/2309.05019.pdf + """ + + assert order in [1, 2, 3, 4], "order of stochastic adams bashforth method is only supported for 1, 2, 3 and 4" + t_fn = lambda sigma: sigma.log().neg() + sigma_prev = sigma_prev_list[-1] + gradient_part = torch.zeros_like(x) + lambda_list = [t_fn(sigma_prev_list[-(i + 1)]) for i in range(order)] + lambda_t = t_fn(sigma) + lambda_prev = lambda_list[0] + h = lambda_t - lambda_prev + gradient_coefficients = get_coefficients_fn(order, lambda_prev, lambda_t, lambda_list, tau) + + if order == 2: ## if order = 2 we do a modification that does not influence the convergence order similar to unipc. Note: This is used only for few steps sampling. + # The added term is O(h^3). Empirically we find it will slightly improve the image quality. + # ODE case + # gradient_coefficients[0] += 1.0 * torch.exp(lambda_t) * (h ** 2 / 2 - (h - 1 + torch.exp(-h))) / (ns.marginal_lambda(t_prev_list[-1]) - ns.marginal_lambda(t_prev_list[-2])) + # gradient_coefficients[1] -= 1.0 * torch.exp(lambda_t) * (h ** 2 / 2 - (h - 1 + torch.exp(-h))) / (ns.marginal_lambda(t_prev_list[-1]) - ns.marginal_lambda(t_prev_list[-2])) + gradient_coefficients[0] += (1.0 * torch.exp((1 + tau ** 2) * lambda_t) + * (h ** 2 / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ((1 + tau ** 2) ** 2)) + / (lambda_prev - lambda_list[1]) + ) + gradient_coefficients[1] -= (1.0 * torch.exp((1 + tau ** 2) * lambda_t) + * (h ** 2 / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) / ((1 + tau ** 2) ** 2)) + / (lambda_prev - lambda_list[1]) + ) + + for i in range(order): + gradient_part += gradient_coefficients[i] * model_prev_list[-(i + 1)] + gradient_part *= (1 + tau ** 2) * sigma * torch.exp(- tau ** 2 * lambda_t) + noise_part = 0 if tau == 0 else sigma * torch.sqrt(1. - torch.exp(-2 * tau ** 2 * h)) * noise + return torch.exp(-tau ** 2 * h) * (sigma / sigma_prev) * x + gradient_part + noise_part + + +def adams_moulton_update_few_steps(order, x, tau, model_prev_list, sigma_prev_list, noise, sigma): + """ + SA-Corrector, with the "rescaling" trick in Appendix D in SA-Solver paper https://arxiv.org/pdf/2309.05019.pdf + """ + + assert order in [1, 2, 3, 4], "order of stochastic adams bashforth method is only supported for 1, 2, 3 and 4" + t_fn = lambda sigma: sigma.log().neg() + sigma_prev = sigma_prev_list[-1] + gradient_part = torch.zeros_like(x) + sigma_list = sigma_prev_list + [sigma] + lambda_list = [t_fn(sigma_list[-(i + 1)]) for i in range(order)] + lambda_t = lambda_list[0] + lambda_prev = lambda_list[1] if order >= 2 else t_fn(sigma_prev) + h = lambda_t - lambda_prev + gradient_coefficients = get_coefficients_fn(order, lambda_prev, lambda_t, lambda_list, tau) + + if order == 2: ## if order = 2 we do a modification that does not influence the convergence order similar to UniPC. Note: This is used only for few steps sampling. + # The added term is O(h^3). Empirically we find it will slightly improve the image quality. + # ODE case + # gradient_coefficients[0] += 1.0 * torch.exp(lambda_t) * (h / 2 - (h - 1 + torch.exp(-h)) / h) + # gradient_coefficients[1] -= 1.0 * torch.exp(lambda_t) * (h / 2 - (h - 1 + torch.exp(-h)) / h) + gradient_coefficients[0] += (1.0 * torch.exp((1 + tau ** 2) * lambda_t) + * (h / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) + / ((1 + tau ** 2) ** 2 * h)) + ) + gradient_coefficients[1] -= (1.0 * torch.exp((1 + tau ** 2) * lambda_t) + * (h / 2 - (h * (1 + tau ** 2) - 1 + torch.exp((1 + tau ** 2) * (-h))) + / ((1 + tau ** 2) ** 2 * h)) + ) + + for i in range(order): + gradient_part += gradient_coefficients[i] * model_prev_list[-(i + 1)] + gradient_part *= (1 + tau ** 2) * sigma * torch.exp(- tau ** 2 * lambda_t) + noise_part = 0 if tau == 0 else sigma * torch.sqrt(1. - torch.exp(-2 * tau ** 2 * h)) * noise + return torch.exp(-tau ** 2 * h) * (sigma / sigma_prev) * x + gradient_part + noise_part + + +def get_tau_interval_func(start_sigma: float, end_sigma: float, eta: float = 1.0) -> Callable[[torch.Tensor], float]: + """Get the function that controls the stochasticity of SA-Solver. + + When eta = 0, SA-Solver runs as ODE. + The official implementation uses t for determining the SDE interval, while this uses sigma instead. + See https://github.com/scxue/SA-Solver/blob/main/README.md + """ + + def tau_func(sigma: Union[torch.Tensor, float]) -> float: + if eta <= 0: + return 0.0 # ODE + + if isinstance(sigma, torch.Tensor): + sigma = sigma.item() + return eta if start_sigma >= sigma >= end_sigma else 0.0 + + return tau_func diff --git a/comfy/k_diffusion/sampling.py b/comfy/k_diffusion/sampling.py index 34218337a..d7d6c5f8a 100644 --- a/comfy/k_diffusion/sampling.py +++ b/comfy/k_diffusion/sampling.py @@ -9,6 +9,7 @@ from tqdm.auto import trange, tqdm from . import utils from . import deis +from . import sa_solver import comfy.model_patcher import comfy.model_sampling @@ -1648,3 +1649,96 @@ def sample_seeds_3(model, x, sigmas, extra_args=None, callback=None, disable=Non if inject_noise: x = x + sigmas[i + 1] * (noise_coeff_3 * noise_1 + noise_coeff_2 * noise_2 + noise_coeff_1 * noise_3) * s_noise return x + + +# Modify from: https://github.com/scxue/SA-Solver +# MIT license +@torch.no_grad() +def sample_sa_solver(model, x, sigmas, extra_args=None, callback=None, disable=False, tau_func=None, noise_sampler=None, predictor_order=3, corrector_order=4, pc_mode="PEC"): + if len(sigmas) <= 1: + return x + + extra_args = {} if extra_args is None else extra_args + if tau_func is None: + model_sampling = model.inner_model.model_patcher.get_model_object('model_sampling') + start_sigma = model_sampling.percent_to_sigma(0.2) + end_sigma = model_sampling.percent_to_sigma(0.8) + tau_func = sa_solver.get_tau_interval_func(start_sigma, end_sigma, eta=1.0) + tau = tau_func + seed = extra_args.get("seed", None) + noise_sampler = default_noise_sampler(x, seed=seed) if noise_sampler is None else noise_sampler + s_in = x.new_ones([x.shape[0]]) + + sigma_prev_list = [] + model_prev_list = [] + + for i in trange(len(sigmas) - 1, disable=disable): + sigma = sigmas[i] + if i == 0: + # Init the initial values + denoised = model(x, sigma * s_in, **extra_args) + model_prev_list.append(denoised) + sigma_prev_list.append(sigma) + else: + # Lower order final + predictor_order_used = min(predictor_order, i, len(sigmas) - i - 1) + corrector_order_used = min(corrector_order, i + 1, len(sigmas) - i + 1) + + tau_val = tau(sigma) + noise = None if tau_val == 0 else noise_sampler(sigma, sigmas[i + 1]) + + # Predictor step + x_p = sa_solver.adams_bashforth_update_few_steps(order=predictor_order_used, x=x, tau=tau_val, + model_prev_list=model_prev_list, sigma_prev_list=sigma_prev_list, + noise=noise, sigma=sigma) + + # Evaluation step + denoised = model(x_p, sigma * s_in, **extra_args) + model_prev_list.append(denoised) + + # Corrector step + if corrector_order_used > 0: + x = sa_solver.adams_moulton_update_few_steps(order=corrector_order_used, x=x, tau=tau_val, + model_prev_list=model_prev_list, sigma_prev_list=sigma_prev_list, + noise=noise, sigma=sigma) + else: + x = x_p + + del noise, x_p + + # Evaluation step for PECE + if corrector_order_used > 0 and pc_mode == 'PECE': + del model_prev_list[-1] + denoised = model(x, sigma * s_in, **extra_args) + model_prev_list.append(denoised) + + sigma_prev_list.append(sigma) + if len(model_prev_list) > max(predictor_order, corrector_order): + del model_prev_list[0] + del sigma_prev_list[0] + + if callback is not None: + callback({'x': x, 'i': i, 'denoised': model_prev_list[-1]}) + + if sigmas[-1] == 0: + # Denoising step + return model_prev_list[-1] + return sa_solver.adams_bashforth_update_few_steps(order=1, x=x, tau=0, model_prev_list=model_prev_list, sigma_prev_list=sigma_prev_list, noise=0, sigma=sigmas[-1]) + +@torch.no_grad() +def sample_sa_solver_pece(model, x, sigmas, extra_args=None, callback=None, disable=False, tau_func=None, noise_sampler=None, predictor_order=3, corrector_order=4): + if len(sigmas) <= 1: + return x + return sample_sa_solver( + model, + x, + sigmas, + extra_args=extra_args, + callback=callback, + disable=disable, + tau_func=tau_func, + noise_sampler=noise_sampler, + predictor_order=predictor_order, + corrector_order=corrector_order, + pc_mode="PECE", + ) diff --git a/comfy/samplers.py b/comfy/samplers.py index 25ccaf39f..e93d2a315 100644 --- a/comfy/samplers.py +++ b/comfy/samplers.py @@ -720,7 +720,7 @@ KSAMPLER_NAMES = ["euler", "euler_cfg_pp", "euler_ancestral", "euler_ancestral_c "lms", "dpm_fast", "dpm_adaptive", "dpmpp_2s_ancestral", "dpmpp_2s_ancestral_cfg_pp", "dpmpp_sde", "dpmpp_sde_gpu", "dpmpp_2m", "dpmpp_2m_cfg_pp", "dpmpp_2m_sde", "dpmpp_2m_sde_gpu", "dpmpp_3m_sde", "dpmpp_3m_sde_gpu", "ddpm", "lcm", "ipndm", "ipndm_v", "deis", "res_multistep", "res_multistep_cfg_pp", "res_multistep_ancestral", "res_multistep_ancestral_cfg_pp", - "gradient_estimation", "gradient_estimation_cfg_pp", "er_sde", "seeds_2", "seeds_3"] + "gradient_estimation", "gradient_estimation_cfg_pp", "er_sde", "seeds_2", "seeds_3", "sa_solver", "sa_solver_pece"] class KSAMPLER(Sampler): def __init__(self, sampler_function, extra_options={}, inpaint_options={}): diff --git a/comfy_extras/nodes_custom_sampler.py b/comfy_extras/nodes_custom_sampler.py index b3a772714..16cb78cff 100644 --- a/comfy_extras/nodes_custom_sampler.py +++ b/comfy_extras/nodes_custom_sampler.py @@ -2,6 +2,7 @@ import math import comfy.samplers import comfy.sample from comfy.k_diffusion import sampling as k_diffusion_sampling +from comfy.k_diffusion import sa_solver from comfy.comfy_types import IO, ComfyNodeABC, InputTypeDict import latent_preview import torch @@ -521,6 +522,38 @@ class SamplerER_SDE(ComfyNodeABC): return (sampler,) +class SamplerSASolver(ComfyNodeABC): + @classmethod + def INPUT_TYPES(cls) -> InputTypeDict: + return {"required": + {"model": (IO.MODEL, {}), + "pc_mode": (IO.COMBO, {"options": ['PEC', "PECE"]},), + "eta": (IO.FLOAT, {"default": 1.0, "min": 0.0, "max": 100.0, "step":0.01, "round": False}), + "eta_start_percent": (IO.FLOAT, {"default": 0.2, "min": 0.0, "max": 1.0, "step": 0.001}), + "eta_end_percent": (IO.FLOAT, {"default": 0.8, "min": 0.0, "max": 1.0, "step": 0.001}), + "predictor_order": (IO.INT, {"default": 3, "min": 1, "max": 4}), + "corrector_order": (IO.INT, {"default": 4, "min": 0, "max": 4}), + } + } + RETURN_TYPES = (IO.SAMPLER,) + CATEGORY = "sampling/custom_sampling/samplers" + + FUNCTION = "get_sampler" + + def get_sampler(self, model, pc_mode, eta, eta_start_percent, eta_end_percent, predictor_order, corrector_order): + model_sampling = model.get_model_object('model_sampling') + start_sigma = model_sampling.percent_to_sigma(eta_start_percent) + end_sigma = model_sampling.percent_to_sigma(eta_end_percent) + tau_func = sa_solver.get_tau_interval_func(start_sigma, end_sigma, eta=eta) + + if pc_mode == 'PEC': + sampler_name = "sa_solver" + else: + sampler_name = "sa_solver_pece" + sampler = comfy.samplers.ksampler(sampler_name, {"tau_func": tau_func, "predictor_order": predictor_order, "corrector_order": corrector_order}) + return (sampler, ) + + class Noise_EmptyNoise: def __init__(self): self.seed = 0 @@ -829,6 +862,7 @@ NODE_CLASS_MAPPINGS = { "SamplerDPMPP_2S_Ancestral": SamplerDPMPP_2S_Ancestral, "SamplerDPMAdaptative": SamplerDPMAdaptative, "SamplerER_SDE": SamplerER_SDE, + "SamplerSASolver": SamplerSASolver, "SplitSigmas": SplitSigmas, "SplitSigmasDenoise": SplitSigmasDenoise, "FlipSigmas": FlipSigmas,