import math
from functools import partial

import logging
from scipy import integrate
import torch
from torch import nn
import torchsde
from tqdm.auto import trange, tqdm

from comfy.k_diffusion import utils
from comfy.k_diffusion import deis

import comfy.model_patcher
import comfy.model_sampling

from comfy.samplers import KSamplerX0Inpaint, Sampler


# =====================================================================
# EasyCache state container
# ---------------------------------------------------------------------
# 参考 EasyCache4HunyuanVideo/easycache_sample_video.py：
#   1) cache = denoised - x （上一次实算时输出与输入的"变换向量"）
#      跳过实算时直接 denoised = x + cache 复用。
#   2) 用一阶线性灵敏度 k = |Δoutput| / |Δinput| 估计跳过该 step 的预测误差
#         pred_change = k * |Δx| / |prev_output|
#      累加为 accumulated_error；< threshold 时继续跳过，否则强制实算并清零。
#   3) 前 ret_steps 步必算（启动保护），最后一步必算（收尾保护）。
# 由于一些 sampler（Heun/DPM-2 等）每 step 内会多次调用 model(...)，
# 这里通过 begin_step/model_call/end_step 三个接口把 EasyCache 状态绑定到外层
# step 索引 i：本 step 的所有 model 调用共享同一个 should_calc 决策。
# =====================================================================
class EasyCacheState:
    def __init__(self, num_steps, threshold=0.025, ret_steps=5):
        self.num_steps = int(num_steps)
        self.threshold = float(threshold)
        self.ret_steps = int(ret_steps)

        self.cnt = 0
        self.should_calc = True
        self.accumulated_error = 0.0

        self.cache = None              # 上一次实算的 (denoised - x)
        self.k = None                  # 灵敏度 |Δoutput|/|Δinput|

        self.previous_raw_input = None
        self.prev_prev_raw_input = None
        self.previous_output = None

        self._step_calc_done = False

    def begin_step(self, i, total_steps, raw_input):
        self.cnt = i
        self._step_calc_done = False
        # 启动 / 收尾保护
        if self.cnt < self.ret_steps or self.cnt >= total_steps - 1:
            self.should_calc = True
            self.accumulated_error = 0.0
            return
        if (self.previous_raw_input is None or self.previous_output is None
                or self.cache is None or self.k is None):
            self.should_calc = True
            return
        raw_input_change = (raw_input - self.previous_raw_input).abs().mean()
        output_norm = self.previous_output.abs().mean().clamp(min=1e-8)
        pred_change = float(self.k) * float(raw_input_change / output_norm)
        self.accumulated_error += pred_change
        if self.accumulated_error < self.threshold:
            self.should_calc = False
        else:
            self.should_calc = True
            self.accumulated_error = 0.0

    def model_call(self, model, x, sigma, **extra_args):
        if (not self.should_calc) and (self.cache is not None):
            return x + self.cache
        denoised = model(x, sigma, **extra_args)
        # 仅在每个 step 第一次实算时更新缓存与灵敏度
        if not self._step_calc_done:
            new_cache = denoised - x
            if self.previous_output is not None and self.prev_prev_raw_input is not None:
                output_change = (denoised - self.previous_output).abs().mean()
                input_change = (self.previous_raw_input - self.prev_prev_raw_input).abs().mean().clamp(min=1e-8)
                self.k = float(output_change / input_change)
            self.cache = new_cache
            self.previous_output = denoised.detach().clone()
            self._step_calc_done = True
        return denoised

    def end_step(self, raw_input):
        self.prev_prev_raw_input = self.previous_raw_input
        self.previous_raw_input = raw_input.detach().clone()


class KSAMPLER(Sampler):
    def __init__(self, sampler_function, threshold, ret_steps, extra_options={}, inpaint_options={}):
        # parameters for EasyCache
        self.threshold = threshold
        self.ret_steps = ret_steps
        self.sampler_function = sampler_function
        self.extra_options = extra_options
        self.inpaint_options = inpaint_options

    def sample(self, model_wrap, sigmas, extra_args, callback, noise, latent_image=None, denoise_mask=None, disable_pbar=False):
        extra_args["denoise_mask"] = denoise_mask
        model_k = KSamplerX0Inpaint(model_wrap, sigmas)
        model_k.latent_image = latent_image
        if self.inpaint_options.get("random", False): #TODO: Should this be the default?
            generator = torch.manual_seed(extra_args.get("seed", 41) + 1)
            model_k.noise = torch.randn(noise.shape, generator=generator, device="cpu").to(noise.dtype).to(noise.device)
        else:
            model_k.noise = noise

        noise = model_wrap.inner_model.model_sampling.noise_scaling(sigmas[0], noise, latent_image, self.max_denoise(model_wrap, sigmas))

        k_callback = None
        total_steps = len(sigmas) - 1
        if callback is not None:
            k_callback = lambda x: callback(x["i"], x["denoised"], x["x"], total_steps)

        samples = self.sampler_function(model_k, noise, sigmas, threshold=self.threshold, ret_steps=self.ret_steps, extra_args=extra_args, callback=k_callback, disable=disable_pbar, **self.extra_options)
        samples = model_wrap.inner_model.model_sampling.inverse_noise_scaling(sigmas[-1], samples)
        return samples
    
def append_zero(x):
    return torch.cat([x, x.new_zeros([1])])

def get_sigmas_karras(n, sigma_min, sigma_max, rho=7., device='cpu'):
    """Constructs the noise schedule of Karras et al. (2022)."""
    ramp = torch.linspace(0, 1, n, device=device)
    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
    return append_zero(sigmas).to(device)

def get_sigmas_exponential(n, sigma_min, sigma_max, device='cpu'):
    """Constructs an exponential noise schedule."""
    sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), n, device=device).exp()
    return append_zero(sigmas)

def get_sigmas_polyexponential(n, sigma_min, sigma_max, rho=1., device='cpu'):
    """Constructs an polynomial in log sigma noise schedule."""
    ramp = torch.linspace(1, 0, n, device=device) ** rho
    sigmas = torch.exp(ramp * (math.log(sigma_max) - math.log(sigma_min)) + math.log(sigma_min))
    return append_zero(sigmas)

def get_sigmas_vp(n, beta_d=19.9, beta_min=0.1, eps_s=1e-3, device='cpu'):
    """Constructs a continuous VP noise schedule."""
    t = torch.linspace(1, eps_s, n, device=device)
    sigmas = torch.sqrt(torch.special.expm1(beta_d * t ** 2 / 2 + beta_min * t))
    return append_zero(sigmas)

def get_sigmas_laplace(n, sigma_min, sigma_max, mu=0., beta=0.5, device='cpu'):
    """Constructs the noise schedule proposed by Tiankai et al. (2024). """
    epsilon = 1e-5 # avoid log(0)
    x = torch.linspace(0, 1, n, device=device)
    clamp = lambda x: torch.clamp(x, min=sigma_min, max=sigma_max)
    lmb = mu - beta * torch.sign(0.5-x) * torch.log(1 - 2 * torch.abs(0.5-x) + epsilon)
    sigmas = clamp(torch.exp(lmb))
    return sigmas

def to_d(x, sigma, denoised):
    """Converts a denoiser output to a Karras ODE derivative."""
    return (x - denoised) / utils.append_dims(sigma, x.ndim)

def get_ancestral_step(sigma_from, sigma_to, eta=1.):
    """Calculates the noise level (sigma_down) to step down to and the amount
    of noise to add (sigma_up) when doing an ancestral sampling step."""
    if not eta:
        return sigma_to, 0.
    sigma_up = min(sigma_to, eta * (sigma_to ** 2 * (sigma_from ** 2 - sigma_to ** 2) / sigma_from ** 2) ** 0.5)
    sigma_down = (sigma_to ** 2 - sigma_up ** 2) ** 0.5
    return sigma_down, sigma_up

def default_noise_sampler(x, seed=None):
    if seed is not None:
        generator = torch.Generator(device=x.device)
        generator.manual_seed(seed)
    else:
        generator = None

    return lambda sigma, sigma_next: torch.randn(x.size(), dtype=x.dtype, layout=x.layout, device=x.device, generator=generator)

class BatchedBrownianTree:
    """A wrapper around torchsde.BrownianTree that enables batches of entropy."""

    def __init__(self, x, t0, t1, seed=None, **kwargs):
        self.cpu_tree = kwargs.pop("cpu", True)
        t0, t1, self.sign = self.sort(t0, t1)
        w0 = kwargs.pop('w0', None)
        if w0 is None:
            w0 = torch.zeros_like(x)
        self.batched = False
        if seed is None:
            seed = (torch.randint(0, 2 ** 63 - 1, ()).item(),)
        elif isinstance(seed, (tuple, list)):
            if len(seed) != x.shape[0]:
                raise ValueError("Passing a list or tuple of seeds to BatchedBrownianTree requires a length matching the batch size.")
            self.batched = True
            w0 = w0[0]
        else:
            seed = (seed,)
        if self.cpu_tree:
            t0, w0, t1 = t0.detach().cpu(), w0.detach().cpu(), t1.detach().cpu()
        self.trees = tuple(torchsde.BrownianTree(t0, w0, t1, entropy=s, **kwargs) for s in seed)

    @staticmethod
    def sort(a, b):
        return (a, b, 1) if a < b else (b, a, -1)

    def __call__(self, t0, t1):
        t0, t1, sign = self.sort(t0, t1)
        device, dtype = t0.device, t0.dtype
        if self.cpu_tree:
            t0, t1 = t0.detach().cpu().float(), t1.detach().cpu().float()
        w = torch.stack([tree(t0, t1) for tree in self.trees]).to(device=device, dtype=dtype) * (self.sign * sign)
        return w if self.batched else w[0]

class BrownianTreeNoiseSampler:
    """A noise sampler backed by a torchsde.BrownianTree.

    Args:
        x (Tensor): The tensor whose shape, device and dtype to use to generate
            random samples.
        sigma_min (float): The low end of the valid interval.
        sigma_max (float): The high end of the valid interval.
        seed (int or List[int]): The random seed. If a list of seeds is
            supplied instead of a single integer, then the noise sampler will
            use one BrownianTree per batch item, each with its own seed.
        transform (callable): A function that maps sigma to the sampler's
            internal timestep.
    """

    def __init__(self, x, sigma_min, sigma_max, seed=None, transform=lambda x: x, cpu=False):
        self.transform = transform
        t0, t1 = self.transform(torch.as_tensor(sigma_min)), self.transform(torch.as_tensor(sigma_max))
        self.tree = BatchedBrownianTree(x, t0, t1, seed, cpu=cpu)

    def __call__(self, sigma, sigma_next):
        t0, t1 = self.transform(torch.as_tensor(sigma)), self.transform(torch.as_tensor(sigma_next))
        return self.tree(t0, t1) / (t1 - t0).abs().sqrt()

def sigma_to_half_log_snr(sigma, model_sampling):
    """Convert sigma to half-logSNR log(alpha_t / sigma_t)."""
    if isinstance(model_sampling, comfy.model_sampling.CONST):
        # log((1 - t) / t) = log((1 - sigma) / sigma)
        return sigma.logit().neg()
    return sigma.log().neg()

def half_log_snr_to_sigma(half_log_snr, model_sampling):
    """Convert half-logSNR log(alpha_t / sigma_t) to sigma."""
    if isinstance(model_sampling, comfy.model_sampling.CONST):
        # 1 / (1 + exp(half_log_snr))
        return half_log_snr.neg().sigmoid()
    return half_log_snr.neg().exp()

def offset_first_sigma_for_snr(sigmas, model_sampling, percent_offset=1e-4):
    """Adjust the first sigma to avoid invalid logSNR."""
    if len(sigmas) <= 1:
        return sigmas
    if isinstance(model_sampling, comfy.model_sampling.CONST):
        if sigmas[0] >= 1:
            sigmas = sigmas.clone()
            sigmas[0] = model_sampling.percent_to_sigma(percent_offset)
    return sigmas

def ei_h_phi_1(h: torch.Tensor) -> torch.Tensor:
    """Compute the result of h*phi_1(h) in exponential integrator methods."""
    return torch.expm1(h)

def ei_h_phi_2(h: torch.Tensor) -> torch.Tensor:
    """Compute the result of h*phi_2(h) in exponential integrator methods."""
    return (torch.expm1(h) - h) / h

def linear_multistep_coeff(order, t, i, j):
    if order - 1 > i:
        raise ValueError(f'Order {order} too high for step {i}')
    def fn(tau):
        prod = 1.
        for k in range(order):
            if j == k:
                continue
            prod *= (tau - t[i - k]) / (t[i - j] - t[i - k])
        return prod
    return integrate.quad(fn, t[i], t[i + 1], epsrel=1e-4)[0]

class PIDStepSizeController:
    """A PID controller for ODE adaptive step size control."""
    def __init__(self, h, pcoeff, icoeff, dcoeff, order=1, accept_safety=0.81, eps=1e-8):
        self.h = h
        self.b1 = (pcoeff + icoeff + dcoeff) / order
        self.b2 = -(pcoeff + 2 * dcoeff) / order
        self.b3 = dcoeff / order
        self.accept_safety = accept_safety
        self.eps = eps
        self.errs = []

    def limiter(self, x):
        return 1 + math.atan(x - 1)

    def propose_step(self, error):
        inv_error = 1 / (float(error) + self.eps)
        if not self.errs:
            self.errs = [inv_error, inv_error, inv_error]
        self.errs[0] = inv_error
        factor = self.errs[0] ** self.b1 * self.errs[1] ** self.b2 * self.errs[2] ** self.b3
        factor = self.limiter(factor)
        accept = factor >= self.accept_safety
        if accept:
            self.errs[2] = self.errs[1]
            self.errs[1] = self.errs[0]
        self.h *= factor
        return accept

class DPMSolver(nn.Module):
    """DPM-Solver. See https://arxiv.org/abs/2206.00927."""

    def __init__(self, model,extra_args=None, eps_callback=None, info_callback=None):
        super().__init__()
        self.model = model
        self.extra_args = {} if extra_args is None else extra_args
        self.eps_callback = eps_callback
        self.info_callback = info_callback

    def t(self, sigma):
        return -sigma.log()

    def sigma(self, t):
        return t.neg().exp()

    def eps(self, eps_cache, key, x, t, final_step = False, *args, **kwargs):
        if key in eps_cache:
            return eps_cache[key], eps_cache
        sigma = self.sigma(t) * x.new_ones([x.shape[0]])
        model_output = self.model(x, sigma, *args, **self.extra_args, **kwargs)        
        eps = (x - model_output) / self.sigma(t)
        if self.eps_callback is not None:
            self.eps_callback()
        return eps, {key: eps, **eps_cache}

    def dpm_solver_1_step(self, x, t, t_next, eps_cache=None,final_step=False):
        eps_cache = {} if eps_cache is None else eps_cache
        h = t_next - t
        eps, eps_cache = self.eps(eps_cache, 'eps', x, t,final_step=final_step)
        x_1 = x - self.sigma(t_next) * h.expm1() * eps
        return x_1, eps_cache

    def dpm_solver_2_step(self, x, t, t_next, r1=1 / 2, eps_cache=None,final_step=False):
        eps_cache = {} if eps_cache is None else eps_cache
        h = t_next - t
        eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
        s1 = t + r1 * h
        u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
        eps_r1, eps_cache = self.eps(eps_cache, 'eps_r1', u1, s1,final_step=final_step)
        x_2 = x - self.sigma(t_next) * h.expm1() * eps - self.sigma(t_next) / (2 * r1) * h.expm1() * (eps_r1 - eps)
        return x_2, eps_cache

    def dpm_solver_3_step(self, x, t, t_next, r1=1 / 3, r2=2 / 3, eps_cache=None,final_step=False):
        eps_cache = {} if eps_cache is None else eps_cache
        h = t_next - t
        eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
        s1 = t + r1 * h
        s2 = t + r2 * h
        u1 = x - self.sigma(s1) * (r1 * h).expm1() * eps
        eps_r1, eps_cache = self.eps(eps_cache, 'eps_r1', u1, s1)
        u2 = x - self.sigma(s2) * (r2 * h).expm1() * eps - self.sigma(s2) * (r2 / r1) * ((r2 * h).expm1() / (r2 * h) - 1) * (eps_r1 - eps)
        eps_r2, eps_cache = self.eps(eps_cache, 'eps_r2', u2, s2,final_step=final_step)
        x_3 = x - self.sigma(t_next) * h.expm1() * eps - self.sigma(t_next) / r2 * (h.expm1() / h - 1) * (eps_r2 - eps)
        return x_3, eps_cache

    def dpm_solver_fast(self, x, t_start, t_end, nfe, eta=0., s_noise=1., noise_sampler=None):
        noise_sampler = default_noise_sampler(x, seed=self.extra_args.get("seed", None)) if noise_sampler is None else noise_sampler
        if not t_end > t_start and eta:
            raise ValueError('eta must be 0 for reverse sampling')
        
        m = math.floor(nfe / 3) + 1
        ts = torch.linspace(t_start, t_end, m + 1, device=x.device)

        if nfe % 3 == 0:
            orders = [3] * (m - 2) + [2, 1]
        else:
            orders = [3] * (m - 1) + [nfe % 3]

        for i in range(len(orders)):
            eps_cache = {}
            t, t_next = ts[i], ts[i + 1]
            if eta:
                sd, su = get_ancestral_step(self.sigma(t), self.sigma(t_next), eta)
                t_next_ = torch.minimum(t_end, self.t(sd))
                su = (self.sigma(t_next) ** 2 - self.sigma(t_next_) ** 2) ** 0.5
            else:
                t_next_, su = t_next, 0.
            
            final_step = True if t_next_ > t_end - 1e-5 else False
            
            eps, eps_cache = self.eps(eps_cache, 'eps', x, t, final_step=final_step)
            denoised = x - self.sigma(t) * eps
            if self.info_callback is not None:
                self.info_callback({'x': x, 'i': i, 't': ts[i], 't_up': t, 'denoised': denoised})

            if orders[i] == 1:
                x, eps_cache = self.dpm_solver_1_step(x, t, t_next_, eps_cache=eps_cache, final_step=final_step)
            elif orders[i] == 2:
                x, eps_cache = self.dpm_solver_2_step(x, t, t_next_, eps_cache=eps_cache, final_step=final_step)
            else:
                x, eps_cache = self.dpm_solver_3_step(x, t, t_next_, eps_cache=eps_cache, final_step=final_step)

            x = x + su * s_noise * noise_sampler(self.sigma(t), self.sigma(t_next))

        return x

    def dpm_solver_adaptive(self, x, t_start, t_end, order=3, rtol=0.05, atol=0.0078, h_init=0.05, pcoeff=0., icoeff=1., dcoeff=0., accept_safety=0.81, eta=0., s_noise=1., noise_sampler=None):
        noise_sampler = default_noise_sampler(x, seed=self.extra_args.get("seed", None)) if noise_sampler is None else noise_sampler
        if order not in {2, 3}:
            raise ValueError('order should be 2 or 3')
        forward = t_end > t_start
        if not forward and eta:
            raise ValueError('eta must be 0 for reverse sampling')
        h_init = abs(h_init) * (1 if forward else -1)
        atol = torch.tensor(atol)
        rtol = torch.tensor(rtol)
        s = t_start
        x_prev = x
        accept = True
        pid = PIDStepSizeController(h_init, pcoeff, icoeff, dcoeff, 1.5 if eta else order, accept_safety)
        info = {'steps': 0, 'nfe': 0, 'n_accept': 0, 'n_reject': 0}

        while s < t_end - 1e-5 if forward else s > t_end + 1e-5:
            eps_cache = {}
            t = torch.minimum(t_end, s + pid.h) if forward else torch.maximum(t_end, s + pid.h)
            if eta:
                sd, su = get_ancestral_step(self.sigma(s), self.sigma(t), eta)
                t_ = torch.minimum(t_end, self.t(sd))
                su = (self.sigma(t) ** 2 - self.sigma(t_) ** 2) ** 0.5
            else:
                t_, su = t, 0.

            if forward:
                final_step = True if t_ > t_end - 1e-5 else False
            else:
                final_step = True if t_ < t_end + 1e-5 else False

            eps, eps_cache = self.eps(eps_cache, 'eps', x, s, final_step=final_step)
            denoised = x - self.sigma(s) * eps
            
            if order == 2:
                x_low, eps_cache = self.dpm_solver_1_step(x, s, t_, eps_cache=eps_cache, final_step=final_step)
                x_high, eps_cache = self.dpm_solver_2_step(x, s, t_, eps_cache=eps_cache, final_step=final_step)
            else:
                x_low, eps_cache = self.dpm_solver_2_step(x, s, t_, r1=1 / 3, eps_cache=eps_cache, final_step=final_step)
                x_high, eps_cache = self.dpm_solver_3_step(x, s, t_, eps_cache=eps_cache, final_step=final_step)
            delta = torch.maximum(atol, rtol * torch.maximum(x_low.abs(), x_prev.abs()))
            error = torch.linalg.norm((x_low - x_high) / delta) / x.numel() ** 0.5
            accept = pid.propose_step(error)
            if accept:
                x_prev = x_low
                x = x_high + su * s_noise * noise_sampler(self.sigma(s), self.sigma(t))
                s = t
                info['n_accept'] += 1
            else:
                info['n_reject'] += 1
            info['nfe'] += order
            info['steps'] += 1

            if self.info_callback is not None:
                self.info_callback({'x': x, 'i': info['steps'] - 1, 't': s, 't_up': s, 'denoised': denoised, 'error': error, 'h': pid.h, **info})

        return x, info

@torch.no_grad()
def sample_euler(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1., threshold=0.025, ret_steps=5):
    """Implements Algorithm 2 (Euler steps) from Karras et al. (2022)."""
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        if s_churn > 0:
            gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
            sigma_hat = sigmas[i] * (gamma + 1)
        else:
            gamma = 0
            sigma_hat = sigmas[i]
        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigma_hat * s_in, **extra_args)
        #-----------------------------------------
        d = to_d(x, sigma_hat, denoised)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
        dt = sigmas[i + 1] - sigma_hat
        # Euler method
        x = x + d * dt
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_heun(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1., threshold=0.025, ret_steps=5):
    """Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        if s_churn > 0:
            gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
            sigma_hat = sigmas[i] * (gamma + 1)
        else:
            gamma = 0
            sigma_hat = sigmas[i]

        sigma_hat = sigmas[i] * (gamma + 1)
        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigma_hat * s_in, **extra_args)
        #-----------------------------------------
        d = to_d(x, sigma_hat, denoised)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
        dt = sigmas[i + 1] - sigma_hat
        if sigmas[i + 1] == 0:
            # Euler method
            x = x + d * dt
        else:
            # Heun's method
            x_2 = x + d * dt
            denoised_2 = ec.model_call(model, x_2, sigmas[i + 1] * s_in, **extra_args)
            d_2 = to_d(x_2, sigmas[i + 1], denoised_2)
            d_prime = (d + d_2) / 2
            x = x + d_prime * dt
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_dpm_2(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1., threshold=0.025, ret_steps=5):
    """A sampler inspired by DPM-Solver-2 and Algorithm 2 from Karras et al. (2022)."""
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        if s_churn > 0:
            gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
            sigma_hat = sigmas[i] * (gamma + 1)
        else:
            gamma = 0
            sigma_hat = sigmas[i]

        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigma_hat * s_in, **extra_args)
        #-----------------------------------------
        d = to_d(x, sigma_hat, denoised)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
        if sigmas[i + 1] == 0:
            # Euler method
            dt = sigmas[i + 1] - sigma_hat
            x = x + d * dt
        else:
            # DPM-Solver-2
            sigma_mid = sigma_hat.log().lerp(sigmas[i + 1].log(), 0.5).exp()
            dt_1 = sigma_mid - sigma_hat
            dt_2 = sigmas[i + 1] - sigma_hat
            x_2 = x + d * dt_1
            denoised_2 = ec.model_call(model, x_2, sigma_mid * s_in, **extra_args)
            d_2 = to_d(x_2, sigma_mid, denoised_2)
            x = x + d_2 * dt_2
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_lms(model, x, sigmas, extra_args=None, callback=None, disable=None, order=4, threshold=0.025, ret_steps=5):
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    sigmas_cpu = sigmas.detach().cpu().numpy()
    ds = []
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        d = to_d(x, sigmas[i], denoised)
        ds.append(d)
        if len(ds) > order:
            ds.pop(0)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        if sigmas[i + 1] == 0:
            # Denoising step
            x = denoised
        else:
            cur_order = min(i + 1, order)
            coeffs = [linear_multistep_coeff(cur_order, sigmas_cpu, i, j) for j in range(cur_order)]
            x = x + sum(coeff * d for coeff, d in zip(coeffs, reversed(ds)))
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_dpm_fast(model, x, sigma_min, sigma_max, n, extra_args=None, callback=None, disable=None, eta=0., s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    """DPM-Solver-Fast (fixed step size). EasyCache 注入到底层 model 调用。"""
    if sigma_min <= 0 or sigma_max <= 0:
        raise ValueError('sigma_min and sigma_max must not be 0')
    #------------add for EasyCache------------
    ec = EasyCacheState(n, threshold=threshold, ret_steps=ret_steps)
    class _ECWrappedModel:
        def __init__(self, base_model):
            self._base = base_model
        def __call__(self, x, sigma, **kw):
            return ec.model_call(self._base, x, sigma, **kw)
    cur_step = {"i": 0}
    #-----------------------------------------
    with tqdm(total=n, disable=disable) as pbar:
        wrapped = _ECWrappedModel(model)
        dpm_solver = DPMSolver(wrapped, extra_args=extra_args, eps_callback=pbar.update)
        def _info(info):
            i = info.get("i", cur_step["i"])
            ec.begin_step(i, n, x)
            ec.end_step(x)
            cur_step["i"] = i + 1
            if callback is not None:
                callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **info})
        dpm_solver.info_callback = _info
        return dpm_solver.dpm_solver_fast(x, dpm_solver.t(torch.tensor(sigma_max)), dpm_solver.t(torch.tensor(sigma_min)), n, eta, s_noise, noise_sampler)

@torch.no_grad()
def sample_dpm_adaptive(model, x, sigma_min, sigma_max, n, extra_args=None, callback=None, disable=None, order=3, rtol=0.05, atol=0.0078, h_init=0.05, pcoeff=0., icoeff=1., dcoeff=0., accept_safety=0.81, eta=0., s_noise=1., noise_sampler=None, return_info=False, threshold=0.025, ret_steps=5):
    """DPM-Solver-12 / 23 (adaptive step size). EasyCache 注入到底层 model 调用。"""
    if sigma_min <= 0 or sigma_max <= 0:
        raise ValueError('sigma_min and sigma_max must not be 0')
    #------------add for EasyCache------------
    ec = EasyCacheState(max(n, 1), threshold=threshold, ret_steps=ret_steps)
    class _ECWrappedModel:
        def __init__(self, base_model):
            self._base = base_model
        def __call__(self, x, sigma, **kw):
            return ec.model_call(self._base, x, sigma, **kw)
    cur_step = {"i": 0}
    #-----------------------------------------
    with tqdm(disable=disable) as pbar:
        wrapped = _ECWrappedModel(model)
        dpm_solver = DPMSolver(wrapped, extra_args=extra_args, eps_callback=pbar.update)
        def _info(info):
            i = info.get("i", cur_step["i"])
            ec.begin_step(i, max(n, 1), x)
            ec.end_step(x)
            cur_step["i"] = i + 1
            if callback is not None:
                callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **info})
        dpm_solver.info_callback = _info
        x_out, info = dpm_solver.dpm_solver_adaptive(x, dpm_solver.t(torch.tensor(sigma_max)), dpm_solver.t(torch.tensor(sigma_min)), order, rtol, atol, h_init, pcoeff, icoeff, dcoeff, accept_safety, eta, s_noise, noise_sampler)
    if return_info:
        return x_out, info
    return x_out

@torch.no_grad()
def sample_dpmpp_2m(model, x, sigmas, extra_args=None, callback=None, disable=None, threshold=0.025, ret_steps=5):
    """DPM-Solver++(2M)."""
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    sigma_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()
    old_denoised = None
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        t, t_next = t_fn(sigmas[i]), t_fn(sigmas[i + 1])
        h = t_next - t
        if old_denoised is None or sigmas[i + 1] == 0:
            x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised
        else:
            h_last = t - t_fn(sigmas[i - 1])
            r = h_last / h
            denoised_d = (1 + 1 / (2 * r)) * denoised - (1 / (2 * r)) * old_denoised
            x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised_d
        old_denoised = denoised
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_heunpp2(model, x, sigmas, extra_args=None, callback=None, disable=None, s_churn=0., s_tmin=0., s_tmax=float('inf'), s_noise=1., threshold=0.025, ret_steps=5):
    # From MIT licensed: https://github.com/Carzit/sd-webui-samplers-scheduler/
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    s_end = sigmas[-1]
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        gamma = min(s_churn / (len(sigmas) - 1), 2 ** 0.5 - 1) if s_tmin <= sigmas[i] <= s_tmax else 0.
        eps = torch.randn_like(x) * s_noise
        sigma_hat = sigmas[i] * (gamma + 1)
        if gamma > 0:
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigma_hat * s_in, **extra_args)
        #-----------------------------------------
        d = to_d(x, sigma_hat, denoised)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigma_hat, 'denoised': denoised})
        dt = sigmas[i + 1] - sigma_hat
        if sigmas[i + 1] == s_end:
            # Euler method
            x = x + d * dt
        elif sigmas[i + 2] == s_end:

            # Heun's method
            x_2 = x + d * dt
            denoised_2 = ec.model_call(model, x_2, sigmas[i + 1] * s_in, **extra_args)
            d_2 = to_d(x_2, sigmas[i + 1], denoised_2)

            w = 2 * sigmas[0]
            w2 = sigmas[i+1]/w
            w1 = 1 - w2

            d_prime = d * w1 + d_2 * w2


            x = x + d_prime * dt

        else:
            # Heun++
            x_2 = x + d * dt
            denoised_2 = ec.model_call(model, x_2, sigmas[i + 1] * s_in, **extra_args)
            d_2 = to_d(x_2, sigmas[i + 1], denoised_2)
            dt_2 = sigmas[i + 2] - sigmas[i + 1]

            x_3 = x_2 + d_2 * dt_2
            denoised_3 = ec.model_call(model, x_3, sigmas[i + 2] * s_in, **extra_args)
            d_3 = to_d(x_3, sigmas[i + 2], denoised_3)

            w = 3 * sigmas[0]
            w2 = sigmas[i + 1] / w
            w3 = sigmas[i + 2] / w
            w1 = 1 - w2 - w3

            d_prime = w1 * d + w2 * d_2 + w3 * d_3
            x = x + d_prime * dt
        ec.end_step(x_step_in)
    return x

#From https://github.com/zju-pi/diff-sampler/blob/main/diff-solvers-main/solvers.py
#under Apache 2 license
def sample_ipndm(model, x, sigmas, extra_args=None, callback=None, disable=None, max_order=4, threshold=0.025, ret_steps=5):
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    x_next = x
    buffer_model = []
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]

        x_cur = x_next

        #------------add for EasyCache------------
        x_step_in = x_cur
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x_cur, t_cur * s_in, **extra_args)
        #-----------------------------------------
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})

        d_cur = (x_cur - denoised) / t_cur

        order = min(max_order, i+1)
        if t_next == 0:     # Denoising step
            x_next = denoised
        elif order == 1:    # First Euler step.
            x_next = x_cur + (t_next - t_cur) * d_cur
        elif order == 2:    # Use one history point.
            x_next = x_cur + (t_next - t_cur) * (3 * d_cur - buffer_model[-1]) / 2
        elif order == 3:    # Use two history points.
            x_next = x_cur + (t_next - t_cur) * (23 * d_cur - 16 * buffer_model[-1] + 5 * buffer_model[-2]) / 12
        elif order == 4:    # Use three history points.
            x_next = x_cur + (t_next - t_cur) * (55 * d_cur - 59 * buffer_model[-1] + 37 * buffer_model[-2] - 9 * buffer_model[-3]) / 24

        if len(buffer_model) == max_order - 1:
            for k in range(max_order - 2):
                buffer_model[k] = buffer_model[k+1]
            buffer_model[-1] = d_cur
        else:
            buffer_model.append(d_cur)
        ec.end_step(x_step_in)
    return x_next

#From https://github.com/zju-pi/diff-sampler/blob/main/diff-solvers-main/solvers.py
#under Apache 2 license
def sample_ipndm_v(model, x, sigmas, extra_args=None, callback=None, disable=None, max_order=4, threshold=0.025, ret_steps=5):
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    x_next = x
    t_steps = sigmas
    buffer_model = []
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]
        x_cur = x_next
        #------------add for EasyCache------------
        x_step_in = x_cur
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x_cur, t_cur * s_in, **extra_args)
        #-----------------------------------------
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        d_cur = (x_cur - denoised) / t_cur
        order = min(max_order, i+1)
        if t_next == 0:     # Denoising step
            x_next = denoised
        elif order == 1:    # First Euler step.
            x_next = x_cur + (t_next - t_cur) * d_cur
        elif order == 2:    # Use one history point.
            h_n = (t_next - t_cur)
            h_n_1 = (t_cur - t_steps[i-1])
            coeff1 = (2 + (h_n / h_n_1)) / 2
            coeff2 = -(h_n / h_n_1) / 2
            x_next = x_cur + (t_next - t_cur) * (coeff1 * d_cur + coeff2 * buffer_model[-1])
        elif order == 3:    # Use two history points.
            h_n = (t_next - t_cur)
            h_n_1 = (t_cur - t_steps[i-1])
            h_n_2 = (t_steps[i-1] - t_steps[i-2])
            temp = (1 - h_n / (3 * (h_n + h_n_1)) * (h_n * (h_n + h_n_1)) / (h_n_1 * (h_n_1 + h_n_2))) / 2
            coeff1 = (2 + (h_n / h_n_1)) / 2 + temp
            coeff2 = -(h_n / h_n_1) / 2 - (1 + h_n_1 / h_n_2) * temp
            coeff3 = temp * h_n_1 / h_n_2
            x_next = x_cur + (t_next - t_cur) * (coeff1 * d_cur + coeff2 * buffer_model[-1] + coeff3 * buffer_model[-2])
        elif order == 4:    # Use three history points.
            h_n = (t_next - t_cur)
            h_n_1 = (t_cur - t_steps[i-1])
            h_n_2 = (t_steps[i-1] - t_steps[i-2])
            h_n_3 = (t_steps[i-2] - t_steps[i-3])
            temp1 = (1 - h_n / (3 * (h_n + h_n_1)) * (h_n * (h_n + h_n_1)) / (h_n_1 * (h_n_1 + h_n_2))) / 2
            temp2 = ((1 - h_n / (3 * (h_n + h_n_1))) / 2 + (1 - h_n / (2 * (h_n + h_n_1))) * h_n / (6 * (h_n + h_n_1 + h_n_2))) \
                   * (h_n * (h_n + h_n_1) * (h_n + h_n_1 + h_n_2)) / (h_n_1 * (h_n_1 + h_n_2) * (h_n_1 + h_n_2 + h_n_3))
            coeff1 = (2 + (h_n / h_n_1)) / 2 + temp1 + temp2
            coeff2 = -(h_n / h_n_1) / 2 - (1 + h_n_1 / h_n_2) * temp1 - (1 + (h_n_1 / h_n_2) + (h_n_1 * (h_n_1 + h_n_2) / (h_n_2 * (h_n_2 + h_n_3)))) * temp2
            coeff3 = temp1 * h_n_1 / h_n_2 + ((h_n_1 / h_n_2) + (h_n_1 * (h_n_1 + h_n_2) / (h_n_2 * (h_n_2 + h_n_3))) * (1 + h_n_2 / h_n_3)) * temp2
            coeff4 = -temp2 * (h_n_1 * (h_n_1 + h_n_2) / (h_n_2 * (h_n_2 + h_n_3))) * h_n_1 / h_n_2
            x_next = x_cur + (t_next - t_cur) * (coeff1 * d_cur + coeff2 * buffer_model[-1] + coeff3 * buffer_model[-2] + coeff4 * buffer_model[-3])
        if len(buffer_model) == max_order - 1:
            for k in range(max_order - 2):
                buffer_model[k] = buffer_model[k+1]
            buffer_model[-1] = d_cur.detach()
        else:
            buffer_model.append(d_cur.detach())
        ec.end_step(x_step_in)

    return x_next

#From https://github.com/zju-pi/diff-sampler/blob/main/diff-solvers-main/solvers.py
#under Apache 2 license
@torch.no_grad()
def sample_deis(model, x, sigmas, extra_args=None, callback=None, disable=None, max_order=3, deis_mode='tab', threshold=0.025, ret_steps=5):
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    x_next = x
    t_steps = sigmas
    coeff_list = deis.get_deis_coeff_list(t_steps, max_order, deis_mode=deis_mode)
    buffer_model = []
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]
        x_cur = x_next
        #------------add for EasyCache------------
        x_step_in = x_cur
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x_cur, t_cur * s_in, **extra_args)
        #-----------------------------------------
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        d_cur = (x_cur - denoised) / t_cur
        order = min(max_order, i+1)
        if t_next <= 0:
            order = 1
        if order == 1:          # First Euler step.
            x_next = x_cur + (t_next - t_cur) * d_cur
        elif order == 2:        # Use one history point.
            coeff_cur, coeff_prev1 = coeff_list[i]
            x_next = x_cur + coeff_cur * d_cur + coeff_prev1 * buffer_model[-1]
        elif order == 3:        # Use two history points.
            coeff_cur, coeff_prev1, coeff_prev2 = coeff_list[i]
            x_next = x_cur + coeff_cur * d_cur + coeff_prev1 * buffer_model[-1] + coeff_prev2 * buffer_model[-2]
        elif order == 4:        # Use three history points.
            coeff_cur, coeff_prev1, coeff_prev2, coeff_prev3 = coeff_list[i]
            x_next = x_cur + coeff_cur * d_cur + coeff_prev1 * buffer_model[-1] + coeff_prev2 * buffer_model[-2] + coeff_prev3 * buffer_model[-3]
        if len(buffer_model) == max_order - 1:
            for k in range(max_order - 2):
                buffer_model[k] = buffer_model[k+1]
            buffer_model[-1] = d_cur.detach()
        else:
            buffer_model.append(d_cur.detach())
        ec.end_step(x_step_in)
    return x_next

@torch.no_grad()
def res_multistep(model, x, sigmas, extra_args=None, callback=None, disable=None, s_noise=1., noise_sampler=None, eta=1., cfg_pp=False, threshold=0.025, ret_steps=5):
    extra_args = {} if extra_args is None else extra_args
    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_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()
    phi1_fn = lambda t: torch.expm1(t) / t
    phi2_fn = lambda t: (phi1_fn(t) - 1.0) / t
    old_sigma_down = None
    old_denoised = None
    uncond_denoised = None
    def post_cfg_function(args):
        nonlocal uncond_denoised
        uncond_denoised = args["uncond_denoised"]
        return args["denoised"]
    if cfg_pp:
        model_options = extra_args.get("model_options", {}).copy()
        extra_args["model_options"] = comfy.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
        if callback is not None:
            callback({"x": x, "i": i, "sigma": sigmas[i], "sigma_hat": sigmas[i], "denoised": denoised})
        if sigma_down == 0 or old_denoised is None:
            # Euler method
            if cfg_pp:
                d = to_d(x, sigmas[i], uncond_denoised)
                x = denoised + d * sigma_down
            else:
                d = to_d(x, sigmas[i], denoised)
                dt = sigma_down - sigmas[i]
                x = x + d * dt
        else:
            # Second order multistep method in https://arxiv.org/pdf/2308.02157
            t, t_old, t_next, t_prev = t_fn(sigmas[i]), t_fn(old_sigma_down), t_fn(sigma_down), t_fn(sigmas[i - 1])
            h = t_next - t
            c2 = (t_prev - t_old) / h
            phi1_val, phi2_val = phi1_fn(-h), phi2_fn(-h)
            b1 = torch.nan_to_num(phi1_val - phi2_val / c2, nan=0.0)
            b2 = torch.nan_to_num(phi2_val / c2, nan=0.0)
            if cfg_pp:
                x = x + (denoised - uncond_denoised)
                x = sigma_fn(h) * x + h * (b1 * uncond_denoised + b2 * old_denoised)
            else:
                x = sigma_fn(h) * x + h * (b1 * denoised + b2 * old_denoised)
        # Noise addition
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
        if cfg_pp:
            old_denoised = uncond_denoised
        else:
            old_denoised = denoised
        old_sigma_down = sigma_down
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_res_multistep(model, x, sigmas, extra_args=None, callback=None, disable=None, s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    return res_multistep(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, s_noise=s_noise, noise_sampler=noise_sampler, eta=0., cfg_pp=False, threshold=threshold, ret_steps=ret_steps)

@torch.no_grad()
def sample_gradient_estimation(model, x, sigmas, extra_args=None, callback=None, disable=None, ge_gamma=2., cfg_pp=False, threshold=0.025, ret_steps=5):
    """Gradient-estimation sampler. Paper: https://openreview.net/pdf?id=o2ND9v0CeK"""
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    old_d = None
    uncond_denoised = None
    def post_cfg_function(args):
        nonlocal uncond_denoised
        uncond_denoised = args["uncond_denoised"]
        return args["denoised"]
    if cfg_pp:
        model_options = extra_args.get("model_options", {}).copy()
        extra_args["model_options"] = comfy.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        if cfg_pp:
            d = to_d(x, sigmas[i], uncond_denoised)
        else:
            d = to_d(x, sigmas[i], denoised)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        dt = sigmas[i + 1] - sigmas[i]
        if sigmas[i + 1] == 0:
            # Denoising step
            x = denoised
        else:
            # Euler method
            if cfg_pp:
                x = denoised + d * sigmas[i + 1]
            else:
                x = x + d * dt
            if i >= 1:
                # Gradient estimation
                d_bar = (ge_gamma - 1) * (d - old_d)
                x = x + d_bar * dt
        old_d = d
        ec.end_step(x_step_in)
    return x

#ancestral、sde方法，可多样性
@torch.no_grad()
def sample_euler_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    if isinstance(model.inner_model.inner_model.model_sampling, comfy.model_sampling.CONST):
        return sample_euler_ancestral_RF(model, x, sigmas, extra_args, callback, disable, eta, s_noise, noise_sampler, threshold=threshold, ret_steps=ret_steps)
    """Ancestral sampling with Euler method steps."""
    extra_args = {} if extra_args is None else extra_args
    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]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})

        if sigma_down == 0:
            x = denoised
        else:
            d = to_d(x, sigmas[i], denoised)
            # Euler method
            dt = sigma_down - sigmas[i]
            x = x + d * dt + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_euler_ancestral_RF(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1.0, s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    """Ancestral sampling with Euler method steps."""
    extra_args = {} if extra_args is None else extra_args
    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]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        # sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})

        if sigmas[i + 1] == 0:
            x = denoised
        else:
            downstep_ratio = 1 + (sigmas[i + 1] / sigmas[i] - 1) * eta
            sigma_down = sigmas[i + 1] * downstep_ratio
            alpha_ip1 = 1 - sigmas[i + 1]
            alpha_down = 1 - sigma_down
            renoise_coeff = (sigmas[i + 1]**2 - sigma_down**2 * alpha_ip1**2 / alpha_down**2)**0.5
            # Euler method
            sigma_down_i_ratio = sigma_down / sigmas[i]
            x = sigma_down_i_ratio * x + (1 - sigma_down_i_ratio) * denoised
            if eta > 0:
                x = (alpha_ip1 / alpha_down) * x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * renoise_coeff
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_dpm_2_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    if isinstance(model.inner_model.inner_model.model_sampling, comfy.model_sampling.CONST):
        return sample_dpm_2_ancestral_RF(model, x, sigmas, extra_args, callback, disable, eta, s_noise, noise_sampler, threshold=threshold, ret_steps=ret_steps)
    """Ancestral sampling with DPM-Solver second-order steps."""
    extra_args = {} if extra_args is None else extra_args
    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]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        sigma_down, sigma_up = get_ancestral_step(sigmas[i], sigmas[i + 1], eta=eta)
        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        d = to_d(x, sigmas[i], denoised)
        if sigma_down == 0:
            # Euler method
            dt = sigma_down - sigmas[i]
            x = x + d * dt
        else:
            # DPM-Solver-2
            sigma_mid = sigmas[i].log().lerp(sigma_down.log(), 0.5).exp()
            dt_1 = sigma_mid - sigmas[i]
            dt_2 = sigma_down - sigmas[i]
            x_2 = x + d * dt_1
            denoised_2 = ec.model_call(model, x_2, sigma_mid * s_in, **extra_args)
            d_2 = to_d(x_2, sigma_mid, denoised_2)
            x = x + d_2 * dt_2
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
        ec.end_step(x_step_in)
    return x

@torch.no_grad()
def sample_dpm_2_ancestral_RF(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, threshold=0.025, ret_steps=5):
    """Ancestral sampling with DPM-Solver second-order steps."""
    extra_args = {} if extra_args is None else extra_args
    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]])
    #------------add for EasyCache------------
    total_steps = len(sigmas) - 1
    ec = EasyCacheState(total_steps, threshold=threshold, ret_steps=ret_steps)
    #-----------------------------------------
    for i in trange(total_steps, disable=disable):
        #------------add for EasyCache------------
        x_step_in = x
        ec.begin_step(i, total_steps, x_step_in)
        denoised = ec.model_call(model, x, sigmas[i] * s_in, **extra_args)
        #-----------------------------------------
        downstep_ratio = 1 + (sigmas[i+1]/sigmas[i] - 1) * eta
        sigma_down = sigmas[i+1] * downstep_ratio
        alpha_ip1 = 1 - sigmas[i+1]
        alpha_down = 1 - sigma_down
        renoise_coeff = (sigmas[i+1]**2 - sigma_down**2*alpha_ip1**2/alpha_down**2)**0.5

        if callback is not None:
            callback({'x': x, 'i': i, 'sigma': sigmas[i], 'sigma_hat': sigmas[i], 'denoised': denoised})
        d = to_d(x, sigmas[i], denoised)
        if sigma_down == 0:
            # Euler method
            dt = sigma_down - sigmas[i]
            x = x + d * dt
        else:
            # DPM-Solver-2
            sigma_mid = sigmas[i].log().lerp(sigma_down.log(), 0.5).exp()
            dt_1 = sigma_mid - sigmas[i]
            dt_2 = sigma_down - sigmas[i]
            x_2 = x + d * dt_1
            denoised_2 = ec.model_call(model, x_2, sigma_mid * s_in, **extra_args)
            d_2 = to_d(x_2, sigma_mid, denoised_2)
            x = x + d_2 * dt_2
            x = (alpha_ip1/alpha_down) * x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * renoise_coeff
        ec.end_step(x_step_in)
    return x