Add SA-Solver

comfy/k_diffusion/sa_solver.py

@@ -0,0 +1,189 @@
+# Modify from: https://github.com/scxue/SA-Solver
+# MIT license
+
+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
+    x_t = torch.exp(-tau ** 2 * h) * (sigma / sigma_prev) * x + gradient_part + noise_part
+    return x_t
+
+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]
+    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
+    x_t = torch.exp(-tau ** 2 * h) * (sigma / sigma_prev) * x + gradient_part + noise_part
+    return x_t
+
+def device_noise_sampler(x, noise_device='gpu'):
+    if noise_device == "gpu":
+        return torch.randn_like(x)
+    else:
+        return torch.randn(x.shape, device='cpu').to(x.device)
+
+# Default tau function from https://github.com/scxue/SA-Solver?tab=readme-ov-file#-abstract
+def default_tau_func(sigma, eta, eta_start_sigma, eta_end_sigma):
+    if eta == 0:
+        # Pure ODE
+        return 0
+    return eta if eta_end_sigma <= sigma <= eta_start_sigma else 0

comfy/k_diffusion/sampling.py

@@ -1,4 +1,5 @@
 import math
+from functools import partial
 
 from scipy import integrate
 import torch
@@ -8,6 +9,7 @@
 
 from . import utils
 from . import deis
+from . import sa_solver
 import comfy.model_patcher
 import comfy.model_sampling
 
@@ -1050,6 +1052,116 @@ def sample_deis(model, x, sigmas, extra_args=None, callback=None, disable=None,
 
     return x_next
 
+# 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, predictor_order=3, corrector_order=4, pc_mode="PEC", tau_func=None, noise_sampler=None):
+    if len(sigmas) <= 1:
+        return x
+
+    if sigmas[-1] == 0:
+        sigmas = sigmas.clone()
+        sigmas[-1] = 0.001
+
+    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 = partial(sa_solver.default_tau_func, eta=1.0, eta_start_sigma=start_sigma, eta_end_sigma=end_sigma)
+    tau = tau_func
+    noise_sampler = partial(sa_solver.device_noise_sampler, x=x, noise_device='cpu') 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)
+            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()
+
+            # 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)
+
+            # Update model_list
+            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 if mode = pece and step != steps
+            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]})
+
+    # Extra final step
+    x = 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])
+    return x
+
+@torch.no_grad()
+def sample_sa_solver_pece(model, x, sigmas, extra_args=None, callback=None, disable=False, predictor_order=3, corrector_order=4, tau_func=None, noise_sampler=None):  
+    if len(sigmas) <= 1:
+        return x
+    return sample_sa_solver(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable,
+                            predictor_order=predictor_order, corrector_order=corrector_order,
+                            pc_mode="PECE", tau_func=tau_func, noise_sampler=noise_sampler,
+                            )
+
+@torch.no_grad()
+def sample_sa_solver_gpu(model, x, sigmas, extra_args=None, callback=None, disable=False, predictor_order=3, corrector_order=4, tau_func=None, noise_sampler=None):
+    if len(sigmas) <= 1:
+        return x
+    noise_sampler = partial(sa_solver.device_noise_sampler, x=x, noise_device='gpu') if noise_sampler is None else noise_sampler
+    return sample_sa_solver(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable,
+                            predictor_order=predictor_order, corrector_order=corrector_order,
+                            pc_mode="PEC", tau_func=tau_func, noise_sampler=noise_sampler,
+                            )
+
+@torch.no_grad()
+def sample_sa_solver_pece_gpu(model, x, sigmas, extra_args=None, callback=None, disable=False, predictor_order=3, corrector_order=4, tau_func=None, noise_sampler=None):
+    if len(sigmas) <= 1:
+        return x
+    noise_sampler = partial(sa_solver.device_noise_sampler, x=x, noise_device='gpu') if noise_sampler is None else noise_sampler
+    return sample_sa_solver(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable,
+                            predictor_order=predictor_order, corrector_order=corrector_order,
+                            pc_mode="PECE", tau_func=tau_func, noise_sampler=noise_sampler,
+                            )
+
 @torch.no_grad()
 def sample_euler_cfg_pp(model, x, sigmas, extra_args=None, callback=None, disable=None):
     extra_args = {} if extra_args is None else extra_args

comfy/samplers.py

@@ -572,7 +572,7 @@ def max_denoise(self, model_wrap, sigmas):
 KSAMPLER_NAMES = ["euler", "euler_cfg_pp", "euler_ancestral", "euler_ancestral_cfg_pp", "heun", "heunpp2","dpm_2", "dpm_2_ancestral",
                   "lms", "dpm_fast", "dpm_adaptive", "dpmpp_2s_ancestral", "dpmpp_2s_ancestral_cfg_pp", "dpmpp_sde", "dpmpp_sde_gpu",
                   "dpmpp_2m", "dpmpp_2m_sde", "dpmpp_2m_sde_gpu", "dpmpp_3m_sde", "dpmpp_3m_sde_gpu", "ddpm", "lcm",
-                  "ipndm", "ipndm_v", "deis"]
+                  "ipndm", "ipndm_v", "deis", 'sa_solver', "sa_solver_gpu", "sa_solver_pece", "sa_solver_pece_gpu"]
 
 class KSAMPLER(Sampler):
     def __init__(self, sampler_function, extra_options={}, inpaint_options={}):