# Taken from https://github.com/comfyanonymous/ComfyUI
# This file is only for reference, and not used in the backend or runtime.


import math

from scipy import integrate
import torch
import numpy as np
from torch import nn
import torchsde
from tqdm.auto import trange, tqdm
import ldm_patched.modules.model_patcher
from ldm_patched.k_diffusion import deis
import torchdiffeq
import modules.shared

from . import utils


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)

# align your steps
def get_sigmas_ays(n, sigma_min, sigma_max, is_sdxl=False, device='cpu'):
    # https://research.nvidia.com/labs/toronto-ai/AlignYourSteps/howto.html
    def loglinear_interp(t_steps, num_steps):
        """
        Performs log-linear interpolation of a given array of decreasing numbers.
        """
        xs = torch.linspace(0, 1, len(t_steps))
        ys = torch.log(torch.tensor(t_steps[::-1]))

        new_xs = torch.linspace(0, 1, num_steps)
        new_ys = np.interp(new_xs, xs, ys)

        interped_ys = torch.exp(torch.tensor(new_ys)).numpy()[::-1].copy()
        return interped_ys

    if is_sdxl:
        sigmas = [14.615, 6.315, 3.771, 2.181, 1.342, 0.862, 0.555, 0.380, 0.234, 0.113, 0.029]
    else:
        # Default to SD 1.5 sigmas.
        sigmas = [14.615, 6.475, 3.861, 2.697, 1.886, 1.396, 0.963, 0.652, 0.399, 0.152, 0.029]

    if n != len(sigmas):
        sigmas = np.append(loglinear_interp(sigmas, n), [0.0])
    else:
        sigmas.append(0.0)

    return torch.FloatTensor(sigmas).to(device)

def get_sigmas_ays_gits(n, sigma_min, sigma_max, is_sdxl=False, device='cpu'):
    def loglinear_interp(t_steps, num_steps):
        xs = torch.linspace(0, 1, len(t_steps))
        ys = torch.log(torch.tensor(t_steps[::-1]))
        new_xs = torch.linspace(0, 1, num_steps)
        new_ys = np.interp(new_xs, xs, ys)
        interped_ys = torch.exp(torch.tensor(new_ys)).numpy()[::-1].copy()
        return interped_ys

    if is_sdxl:
        sigmas = [14.615, 4.734, 2.567, 1.529, 0.987, 0.652, 0.418, 0.268, 0.179, 0.127, 0.029]
    else:
        sigmas = [14.615, 4.617, 2.507, 1.236, 0.702, 0.402, 0.240, 0.156, 0.104, 0.094, 0.029]

    if n != len(sigmas):
        sigmas = np.append(loglinear_interp(sigmas, n), [0.0])
    else:
        sigmas.append(0.0)

    return torch.FloatTensor(sigmas).to(device)

def get_sigmas_ays_11steps(n, sigma_min, sigma_max, is_sdxl=False, device='cpu'):
    # This is the same as the original AYS
    return get_sigmas_ays(n, sigma_min, sigma_max, is_sdxl, device)

def get_sigmas_ays_32steps(n, sigma_min, sigma_max, is_sdxl=False, device='cpu'):
    def loglinear_interp(t_steps, num_steps):
        xs = torch.linspace(0, 1, len(t_steps))
        ys = torch.log(torch.tensor(t_steps[::-1]))
        new_xs = torch.linspace(0, 1, num_steps)
        new_ys = np.interp(new_xs, xs, ys)
        interped_ys = torch.exp(torch.tensor(new_ys)).numpy()[::-1].copy()
        return interped_ys
    
    if is_sdxl:
        sigmas = [14.61500000000000000, 11.14916180000000000, 8.505221270000000000, 6.488271510000000000, 5.437074020000000000, 4.603986190000000000, 3.898547040000000000, 3.274074570000000000, 2.743965270000000000, 2.299686590000000000, 1.954485140000000000, 1.671087150000000000, 1.428781520000000000, 1.231810090000000000, 1.067896490000000000, 0.925794430000000000, 0.802908860000000000, 0.696601210000000000, 0.604369030000000000, 0.528525520000000000, 0.467733440000000000, 0.413933790000000000, 0.362581860000000000, 0.310085170000000000, 0.265189250000000000, 0.223264610000000000, 0.176538770000000000, 0.139591920000000000, 0.105873810000000000, 0.055193690000000000, 0.028773340000000000, 0.015000000000000000]
    else:
        sigmas = [14.61500000000000000, 11.23951352000000000, 8.643630810000000000, 6.647294240000000000, 5.572508620000000000, 4.716485460000000000, 3.991960650000000000, 3.519560900000000000, 3.134904660000000000, 2.792287880000000000, 2.487736280000000000, 2.216638650000000000, 1.975083510000000000, 1.779317200000000000, 1.614753350000000000, 1.465409530000000000, 1.314849000000000000, 1.166424970000000000, 1.034755470000000000, 0.915737440000000000, 0.807481690000000000, 0.712023610000000000, 0.621739000000000000, 0.530652020000000000, 0.452909600000000000, 0.374914550000000000, 0.274618190000000000, 0.201152900000000000, 0.141058730000000000, 0.066828810000000000, 0.031661210000000000, 0.015000000000000000]
    
    if n != len(sigmas):
        sigmas = np.append(loglinear_interp(sigmas, n), [0.0])
    else:
        sigmas.append(0.0)
    
    return torch.FloatTensor(sigmas).to(device)

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.exp(beta_d * t ** 2 / 2 + beta_min * t) - 1)
    return append_zero(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):
    return lambda sigma, sigma_next: torch.randn_like(x)

ADAPTIVE_SOLVERS = {"dopri8", "dopri5", "bosh3", "fehlberg2", "adaptive_heun"}
FIXED_SOLVERS = {"euler", "midpoint", "rk4", "heun3", "explicit_adams", "implicit_adams"}
ALL_SOLVERS = list(ADAPTIVE_SOLVERS | FIXED_SOLVERS)
ALL_SOLVERS.sort()
class ODEFunction:
    def __init__(self, model, t_min, t_max, n_steps, is_adaptive, extra_args=None, callback=None):
        self.model = model
        self.extra_args = {} if extra_args is None else extra_args
        self.callback = callback
        self.t_min = t_min.item()
        self.t_max = t_max.item()
        self.n_steps = n_steps
        self.is_adaptive = is_adaptive
        self.step = 0

        if is_adaptive:
            self.pbar = tqdm(
                total=100,
                desc="solve",
                unit="%",
                leave=False,
                position=1
            )
        else:
            self.pbar = tqdm(
                total=n_steps,
                desc="solve",
                leave=False,
                position=1
            )

    def __call__(self, t, y):
        if t <= 1e-5:
            return torch.zeros_like(y)

        denoised = self.model(y.unsqueeze(0), t.unsqueeze(0), **self.extra_args)
        return (y - denoised.squeeze(0)) / t

    def _callback(self, t0, y0, step):
        if self.callback is not None:
            y0 = y0.unsqueeze(0)

            self.callback({
                "x": y0,
                "i": step,
                "sigma": t0,
                "sigma_hat": t0,
                "denoised": y0, # for a bad latent preview
            })

    def callback_step(self, t0, y0, dt):
        if self.is_adaptive:
            return

        self._callback(t0, y0, self.step)

        self.pbar.update(1)
        self.step += 1

    def callback_accept_step(self, t0, y0, dt):
        if not self.is_adaptive:
            return

        progress = (self.t_max - t0.item()) / (self.t_max - self.t_min)

        self._callback(t0, y0, round((self.n_steps - 1) * progress))

        new_step = round(100 * progress)
        self.pbar.update(new_step - self.step)
        self.step = new_step

    def reset(self):
        self.step = 0
        self.pbar.reset()

class ODESampler:
    def __init__(self, solver, rtol, atol, max_steps):
        self.solver = solver
        self.rtol = rtol
        self.atol = atol
        self.max_steps = max_steps

    @torch.no_grad()
    def __call__(self, model, x: torch.Tensor, sigmas: torch.Tensor, extra_args=None, callback=None, disable=None):
        t_max = sigmas.max()
        t_min = sigmas.min()
        n_steps = len(sigmas)

        if self.solver in FIXED_SOLVERS:
            t = sigmas
            is_adaptive = False
        else:
            t = torch.stack([t_max, t_min])
            is_adaptive = True

        ode = ODEFunction(model, t_min, t_max, n_steps, is_adaptive=is_adaptive, callback=callback, extra_args=extra_args)

        samples = torch.empty_like(x)
        for i in trange(x.shape[0], desc=self.solver, disable=disable):
            ode.reset()

            samples[i] = torchdiffeq.odeint(
                ode,
                x[i],
                t,
                rtol=self.rtol,
                atol=self.atol,
                method=self.solver,
                options={
                    "min_step": 1e-5,
                    "max_num_steps": self.max_steps,
                    "dtype": torch.float32 if torch.backends.mps.is_available() else torch.float64
                }
            )[-1]

        if callback is not None:
            callback({
                "x": samples,
                "i": n_steps - 1,
                "sigma": t_min,
                "sigma_hat": t_min,
                "denoised": samples, # only accurate if t_min = 0, for now
            })

        return samples


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

    def __init__(self, x, t0, t1, seed=None, **kwargs):
        self.cpu_tree = True
        if "cpu" in kwargs:
            self.cpu_tree = kwargs.pop("cpu")
        t0, t1, self.sign = self.sort(t0, t1)
        w0 = kwargs.get('w0', torch.zeros_like(x))
        if seed is None:
            seed = torch.randint(0, 2 ** 63 - 1, []).item()
        self.batched = True
        try:
            assert len(seed) == x.shape[0]
            w0 = w0[0]
        except TypeError:
            seed = [seed]
            self.batched = False
        if self.cpu_tree:
            self.trees = [torchsde.BrownianTree(t0.cpu(), w0.cpu(), t1.cpu(), entropy=s, **kwargs) for s in seed]
        else:
            self.trees = [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)
        if self.cpu_tree:
            w = torch.stack([tree(t0.cpu().float(), t1.cpu().float()).to(t0.dtype).to(t0.device) for tree in self.trees]) * (self.sign * sign)
        else:
            w = torch.stack([tree(t0, t1) for tree in self.trees]) * (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()


@torch.no_grad()
def sample_euler(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """Implements Algorithm 2 (Euler steps) from Karras et al. (2022)."""
    s_churn = modules.shared.opts.euler_og_s_churn
    s_tmin = modules.shared.opts.euler_og_s_tmin
    s_noise = modules.shared.opts.euler_og_s_noise
    s_tmax = float('inf')

    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        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)
        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        denoised = 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
        x = x + d * dt
    return x

@torch.no_grad()
def sample_euler_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    """Ancestral sampling with Euler method steps."""
    eta = modules.shared.opts.euler_ancestral_og_eta
    s_noise = modules.shared.opts.euler_ancestral_og_s_noise

    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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)
        # Euler method
        dt = sigma_down - sigmas[i]
        x = x + d * dt
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_heun(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """Implements Algorithm 2 (Heun steps) from Karras et al. (2022)."""
    s_churn = modules.shared.opts.heun_og_s_churn
    s_tmin = modules.shared.opts.heun_og_s_tmin
    s_noise = modules.shared.opts.heun_og_s_noise
    s_tmax = float('inf')

    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        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)
        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        denoised = 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:
            x = x + d * dt
        else:
            x_2 = x + d * dt
            denoised_2 = 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
    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.):
    """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]])
    for i in trange(len(sigmas) - 1, disable=disable):
        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)
        if gamma > 0:
            eps = torch.randn_like(x) * s_noise
            x = x + eps * (sigma_hat ** 2 - sigmas[i] ** 2) ** 0.5
        denoised = 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 = 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
    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):
    """Ancestral sampling with DPM-Solver second-order steps."""
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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 = 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
    return x


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]


@torch.no_grad()
def sample_lms(model, x, sigmas, extra_args=None, callback=None, disable=None, order=4):
    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 = []
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        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)))
    return x


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, *args, **kwargs):
        if key in eps_cache:
            return eps_cache[key], eps_cache
        sigma = self.sigma(t) * x.new_ones([x.shape[0]])
        eps = (x - self.model(x, sigma, *args, **self.extra_args, **kwargs)) / 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):
        eps_cache = {} if eps_cache is None else eps_cache
        h = t_next - t
        eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
        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):
        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)
        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):
        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)
        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) 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.

            eps, eps_cache = self.eps(eps_cache, 'eps', x, t)
            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)
            elif orders[i] == 2:
                x, eps_cache = self.dpm_solver_2_step(x, t, t_next_, eps_cache=eps_cache)
            else:
                x, eps_cache = self.dpm_solver_3_step(x, t, t_next_, eps_cache=eps_cache)

            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) 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.

            eps, eps_cache = self.eps(eps_cache, 'eps', x, s)
            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)
                x_high, eps_cache = self.dpm_solver_2_step(x, s, t_, eps_cache=eps_cache)
            else:
                x_low, eps_cache = self.dpm_solver_2_step(x, s, t_, r1=1 / 3, eps_cache=eps_cache)
                x_high, eps_cache = self.dpm_solver_3_step(x, s, t_, eps_cache=eps_cache)
            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_dpm_fast(model, x, sigma_min, sigma_max, n, extra_args=None, callback=None, disable=None, eta=0., s_noise=1., noise_sampler=None):
    """DPM-Solver-Fast (fixed step size). See https://arxiv.org/abs/2206.00927."""
    if sigma_min <= 0 or sigma_max <= 0:
        raise ValueError('sigma_min and sigma_max must not be 0')
    with tqdm(total=n, disable=disable) as pbar:
        dpm_solver = DPMSolver(model, extra_args, eps_callback=pbar.update)
        if callback is not None:
            dpm_solver.info_callback = lambda info: callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **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, 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):
    """DPM-Solver-12 and 23 (adaptive step size). See https://arxiv.org/abs/2206.00927."""
    if sigma_min <= 0 or sigma_max <= 0:
        raise ValueError('sigma_min and sigma_max must not be 0')
    with tqdm(disable=disable) as pbar:
        dpm_solver = DPMSolver(model, extra_args, eps_callback=pbar.update)
        if callback is not None:
            dpm_solver.info_callback = lambda info: callback({'sigma': dpm_solver.sigma(info['t']), 'sigma_hat': dpm_solver.sigma(info['t_up']), **info})
        x, 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, info
    return x

@torch.no_grad()
def sample_dpmpp_2s_ancestral(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    """Ancestral sampling with DPM-Solver++(2S) second-order steps."""
    eta = modules.shared.opts.dpm_2s_ancestral_og_eta
    s_noise = modules.shared.opts.dpm_2s_ancestral_og_s_noise

    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) 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()

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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:
            # Euler method
            d = to_d(x, sigmas[i], denoised)
            dt = sigma_down - sigmas[i]
            x = x + d * dt
        else:
            # DPM-Solver++(2S)
            t, t_next = t_fn(sigmas[i]), t_fn(sigma_down)
            r = 1 / 2
            h = t_next - t
            s = t + r * h
            x_2 = (sigma_fn(s) / sigma_fn(t)) * x - (-h * r).expm1() * denoised
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
            x = (sigma_fn(t_next) / sigma_fn(t)) * x - (-h).expm1() * denoised_2
        # Noise addition
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_dpmpp_sde(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """DPM-Solver++ (stochastic)."""
    eta = modules.shared.opts.dpmpp_sde_og_eta
    s_noise = modules.shared.opts.dpmpp_sde_og_s_noise
    r = modules.shared.opts.dpmpp_sde_og_r
    
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=True)
    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()
    
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        if sigmas[i + 1] == 0:
            # Euler method
            d = to_d(x, sigmas[i], denoised)
            dt = sigmas[i + 1] - sigmas[i]
            x = x + d * dt
        else:
            # DPM-Solver++
            t, t_next = t_fn(sigmas[i]), t_fn(sigmas[i + 1])
            h = t_next - t
            s = t + h * r
            fac = 1 / (2 * r)
            # Step 1
            sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(s), eta)
            s_ = t_fn(sd)
            x_2 = (sigma_fn(s_) / sigma_fn(t)) * x - (t - s_).expm1() * denoised
            x_2 = x_2 + noise_sampler(sigma_fn(t), sigma_fn(s)) * s_noise * su
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
            # Step 2
            sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(t_next), eta)
            t_next_ = t_fn(sd)
            denoised_d = (1 - fac) * denoised + fac * denoised_2
            x = (sigma_fn(t_next_) / sigma_fn(t)) * x - (t - t_next_).expm1() * denoised_d
            x = x + noise_sampler(sigma_fn(t), sigma_fn(t_next)) * s_noise * su
    return x


@torch.no_grad()
def sample_dpmpp_2m(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """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
    
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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
    return x

@torch.no_grad()
def sample_dpmpp_2m_sde(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """DPM-Solver++(2M) SDE."""
    eta = modules.shared.opts.dpmpp_2m_sde_og_eta
    s_noise = modules.shared.opts.dpmpp_2m_sde_og_s_noise
    solver_type = modules.shared.opts.dpmpp_2m_sde_og_solver_type
    
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=True)
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    old_denoised = None
    h_last = None
    h = None
    
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        if sigmas[i + 1] == 0:
            # Denoising step
            x = denoised
        else:
            # DPM-Solver++(2M) SDE
            t, s = -sigmas[i].log(), -sigmas[i + 1].log()
            h = s - t
            eta_h = eta * h
            x = sigmas[i + 1] / sigmas[i] * (-eta_h).exp() * x + (-h - eta_h).expm1().neg() * denoised
            if old_denoised is not None:
                r = h_last / h
                if solver_type == 'heun':
                    x = x + ((-h - eta_h).expm1().neg() / (-h - eta_h) + 1) * (1 / r) * (denoised - old_denoised)
                elif solver_type == 'midpoint':
                    x = x + 0.5 * (-h - eta_h).expm1().neg() * (1 / r) * (denoised - old_denoised)
            if eta:
                x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * sigmas[i + 1] * (-2 * eta_h).expm1().neg().sqrt() * s_noise
        old_denoised = denoised
        h_last = h
    return x

@torch.no_grad()
def sample_dpmpp_3m_sde(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """DPM-Solver++(3M) SDE."""
    eta = modules.shared.opts.dpmpp_3m_sde_og_eta
    s_noise = modules.shared.opts.dpmpp_3m_sde_og_s_noise
    
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=True)
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    denoised_1, denoised_2 = None, None
    h, h_1, h_2 = None, None, None
    
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        if sigmas[i + 1] == 0:
            # Denoising step
            x = denoised
        else:
            t, s = -sigmas[i].log(), -sigmas[i + 1].log()
            h = s - t
            h_eta = h * (eta + 1)
            x = torch.exp(-h_eta) * x + (-h_eta).expm1().neg() * denoised
            if h_2 is not None:
                r0 = h_1 / h
                r1 = h_2 / h
                d1_0 = (denoised - denoised_1) / r0
                d1_1 = (denoised_1 - denoised_2) / r1
                d1 = d1_0 + (d1_0 - d1_1) * r0 / (r0 + r1)
                d2 = (d1_0 - d1_1) / (r0 + r1)
                phi_2 = h_eta.neg().expm1() / h_eta + 1
                phi_3 = phi_2 / h_eta - 0.5
                x = x + phi_2 * d1 - phi_3 * d2
            elif h_1 is not None:
                r = h_1 / h
                d = (denoised - denoised_1) / r
                phi_2 = h_eta.neg().expm1() / h_eta + 1
                x = x + phi_2 * d
            if eta:
                x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * sigmas[i + 1] * (-2 * h * eta).expm1().neg().sqrt() * s_noise
        denoised_1, denoised_2 = denoised, denoised_1
        h_1, h_2 = h, h_1
    return x

@torch.no_grad()
def sample_dpmpp_3m_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
    return sample_dpmpp_3m_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler)

@torch.no_grad()
def sample_dpmpp_2m_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, solver_type='midpoint'):
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
    return sample_dpmpp_2m_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler, solver_type=solver_type)

@torch.no_grad()
def sample_dpmpp_sde_gpu(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None, r=1 / 2):
    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=extra_args.get("seed", None), cpu=False) if noise_sampler is None else noise_sampler
    return sample_dpmpp_sde(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable, eta=eta, s_noise=s_noise, noise_sampler=noise_sampler, r=r)


def DDPMSampler_step(x, sigma, sigma_prev, noise, noise_sampler):
    alpha_cumprod = 1 / ((sigma * sigma) + 1)
    alpha_cumprod_prev = 1 / ((sigma_prev * sigma_prev) + 1)
    alpha = (alpha_cumprod / alpha_cumprod_prev)

    mu = (1.0 / alpha).sqrt() * (x - (1 - alpha) * noise / (1 - alpha_cumprod).sqrt())
    if sigma_prev > 0:
        mu += ((1 - alpha) * (1. - alpha_cumprod_prev) / (1. - alpha_cumprod)).sqrt() * noise_sampler(sigma, sigma_prev)
    return mu

def generic_step_sampler(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None, step_function=None):
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    s_in = x.new_ones([x.shape[0]])

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        x = step_function(x / torch.sqrt(1.0 + sigmas[i] ** 2.0), sigmas[i], sigmas[i + 1], (x - denoised) / sigmas[i], noise_sampler)
        if sigmas[i + 1] != 0:
            x *= torch.sqrt(1.0 + sigmas[i + 1] ** 2.0)
    return x


@torch.no_grad()
def sample_ddpm(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    return generic_step_sampler(model, x, sigmas, extra_args, callback, disable, noise_sampler, DDPMSampler_step)

@torch.no_grad()
def sample_lcm(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})

        x = denoised
        if sigmas[i + 1] > 0:
            x += sigmas[i + 1] * noise_sampler(sigmas[i], sigmas[i + 1])
    return x



@torch.no_grad()
def sample_heunpp2(model, x, sigmas, extra_args=None, callback=None, disable=None):
    s_churn = modules.shared.opts.heunpp2_s_churn
    s_tmin = modules.shared.opts.heunpp2_s_tmin
    s_noise = modules.shared.opts.heunpp2_s_noise
    s_tmax = float('inf')
    
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    s_end = sigmas[-1]
    for i in trange(len(sigmas) - 1, 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
        denoised = 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 = 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 = 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 = 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
    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 = modules.shared.opts.ipndm_max_order
    
    extra_args = {} if extra_args is None else extra_args
    s_in = x.new_ones([x.shape[0]])
    x_next = x
    buffer_model = []
    for i in trange(len(sigmas) - 1, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]
        x_cur = x_next
        denoised = 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 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)
    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 = modules.shared.opts.ipndm_v_max_order
    
    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 = []
    for i in trange(len(sigmas) - 1, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]
        x_cur = x_next
        denoised = 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 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())
    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()
@torch.no_grad()
def sample_deis(model, x, sigmas, extra_args=None, callback=None, disable=None):
    max_order = modules.shared.opts.deis_max_order
    deis_mode = modules.shared.opts.deis_mode
    
    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 = []
    for i in trange(len(sigmas) - 1, disable=disable):
        t_cur = sigmas[i]
        t_next = sigmas[i + 1]
        x_cur = x_next
        denoised = 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())
    return x_next

@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

    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]

    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)

    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        sigma_hat = sigmas[i]
        denoised = model(x, sigma_hat * s_in, **extra_args)
        d = to_d(x, sigma_hat, temp[0])
        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 = denoised + d * sigmas[i + 1]
    return x

@torch.no_grad()
def sample_euler_ancestral_cfg_pp(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    """Ancestral sampling with Euler method steps."""
    eta = modules.shared.opts.euler_ancestral_eta
    s_noise = modules.shared.opts.euler_ancestral_s_noise
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler

    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]

    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)

    s_in = x.new_ones([x.shape[0]])
    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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], temp[0])
        # Euler method
        dt = sigma_down - sigmas[i]
        x = denoised + d * sigma_down
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_dpmpp_2s_ancestral_cfg_pp(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    """Ancestral sampling with DPM-Solver++(2S) second-order steps and CFG++."""
    eta = modules.shared.opts.dpmpp_2s_ancestral_eta
    s_noise = modules.shared.opts.dpmpp_2s_ancestral_s_noise
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    
    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]
    
    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
    
    s_in = x.new_ones([x.shape[0]])
    sigma_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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:
            # Euler method
            d = to_d(x, sigmas[i], temp[0])
            dt = sigma_down - sigmas[i]
            x = denoised + d * sigma_down
        else:
            # DPM-Solver++(2S)
            t, t_next = t_fn(sigmas[i]), t_fn(sigma_down)
            r = 1 / 2
            h = t_next - t
            s = t + r * h
            x_2 = (sigma_fn(s) / sigma_fn(t)) * x - (-h * r).expm1() * denoised
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
            d = to_d(x, sigmas[i], temp[0])
            x = denoised_2 + d * sigma_down
        # Noise addition
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_dpmpp_2s_ancestral_cfg_pp_dyn(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
    """Ancestral sampling with DPM-Solver++(2S) second-order steps."""
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    
    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]

    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)

    s_in = x.new_ones([x.shape[0]])
    sigma_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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:
            # Euler method
            d = to_d(x, sigmas[i], temp[0])
            dt = sigma_down - sigmas[i]
            x = denoised + d * sigma_down
        else:
            # DPM-Solver++(2S)
            t, t_next = t_fn(sigmas[i]), t_fn(sigma_down)
            r = torch.sinh(1 + (2 - eta) * (t_next - t) / (t - t_fn(sigma_up)))
            h = t_next - t
            s = t + r * h
            x_2 = (sigma_fn(s) / sigma_fn(t)) * (x + (denoised - temp[0])) - (-h * r).expm1() * denoised
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
            x = (sigma_fn(t_next) / sigma_fn(t)) * (x + (denoised - temp[0])) - (-h).expm1() * denoised_2
        # Noise addition
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_dpmpp_2s_ancestral_cfg_pp_intern(model, x, sigmas, extra_args=None, callback=None, disable=None, eta=1., s_noise=1., noise_sampler=None):
    """Ancestral sampling with DPM-Solver++(2S) second-order steps."""
    extra_args = {} if extra_args is None else extra_args
    noise_sampler = default_noise_sampler(x) if noise_sampler is None else noise_sampler
    
    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]

    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)

    s_in = x.new_ones([x.shape[0]])
    sigma_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()
    s = sigmas[0]
    small_x = nn.functional.interpolate(x, scale_factor=0.5, mode='area')
    den = model(small_x, s * s_in, **extra_args)
    den = nn.functional.interpolate(den, scale_factor=2, mode='area')
    ups_temp = nn.functional.interpolate(temp[0], scale_factor=2, mode='area')
    sigma_down, sigma_up = get_ancestral_step(s, sigmas[1], eta=eta)
    t, t_next = t_fn(s), t_fn(sigma_down)
    r = 1 / 2
    h = t_next - t
    s_ = t + r * h
    x_2 = (sigma_fn(s_) / sigma_fn(t)) * (x + (den - ups_temp)) - (-h * r).expm1() * den
    denoised_2 = model(x_2, sigma_fn(s_) * s_in, **extra_args)
    x = (sigma_fn(t_next) / sigma_fn(t)) * (x + (den - temp[0])) - (-h).expm1() * denoised_2
    large_denoised = x
    x = x + noise_sampler(sigmas[0], sigmas[1]) * s_noise * sigma_up
    sigmas = sigmas[1:] # remove the first sigma we used
    for i in trange(len(sigmas) - 2, disable=disable):
        if sigma_down != 0:
            down_x = nn.functional.interpolate(x, scale_factor=0.5, mode='area')
            denoised = model(down_x, sigmas[i] * s_in, **extra_args)
        else:
            denoised = model(x, sigmas[i] * s_in, **extra_args)
        # denoised = 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:
            # Euler method
            d = to_d(x, sigmas[i], temp[0])
            x = denoised + d * sigma_down
        else:
            # DPM-Solver++(2S)
            t, t_next = t_fn(sigmas[i]), t_fn(sigma_down)
            r = 1 / 2
            h = t_next - t
            s = t + r * h
            mergefactor = min(math.sqrt(i/(len(sigmas) - 2)), 1) 
            print(mergefactor)
            #merge up_den with x
            if mergefactor == 1:
                up_den = large_denoised
                up_temp = nn.functional.interpolate(temp[0], scale_factor=2, mode='area')
                x_2 = (sigma_fn(s) / sigma_fn(t)) * (x + (up_den - up_temp)) - (-h * r).expm1() * up_den
            else:
                up_den = nn.functional.interpolate(denoised, scale_factor=2, mode='area')
                print(up_den.max(), large_denoised.max())
                up_den = (up_den * (1-mergefactor)) + (large_denoised * mergefactor)
                print(up_den.max(), large_denoised.max())
                up_temp = nn.functional.interpolate(temp[0], scale_factor=2, mode='area')
                x_2 = (sigma_fn(s) / sigma_fn(t)) * (x + (up_den - up_temp)) - (-h * r).expm1() * up_den
            
            
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)
            x = (sigma_fn(t_next) / sigma_fn(t)) * (x + (up_den - temp[0])) - (-h).expm1() * denoised_2
            large_denoised = denoised_2
        # Noise addition
        if sigmas[i + 1] > 0:
            x = x + noise_sampler(sigmas[i], sigmas[i + 1]) * s_noise * sigma_up
    return x

@torch.no_grad()
def sample_dpmpp_sde_cfg_pp(model, x, sigmas, extra_args=None, callback=None, disable=None, noise_sampler=None):
    """DPM-Solver++ (stochastic) with CFG++."""
    eta = modules.shared.opts.dpmpp_sde_eta
    s_noise = modules.shared.opts.dpmpp_sde_s_noise
    r = modules.shared.opts.dpmpp_sde_r
    if len(sigmas) <= 1:
        return x

    sigma_min, sigma_max = sigmas[sigmas > 0].min(), sigmas.max()
    seed = extra_args.get("seed", None)
    noise_sampler = BrownianTreeNoiseSampler(x, sigma_min, sigma_max, seed=seed, cpu=True) if noise_sampler is None else noise_sampler
    extra_args = {} if extra_args is None else extra_args
    
    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]
    
    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
    
    s_in = x.new_ones([x.shape[0]])
    sigma_fn = lambda t: t.neg().exp()
    t_fn = lambda sigma: sigma.log().neg()

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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})
        if sigmas[i + 1] == 0:
            # Euler method
            d = to_d(x, sigmas[i], temp[0])
            dt = sigmas[i + 1] - sigmas[i]
            x = denoised + d * sigmas[i + 1]
        else:
            # DPM-Solver++
            t, t_next = t_fn(sigmas[i]), t_fn(sigmas[i + 1])
            h = t_next - t
            s = t + h * r
            fac = 1 / (2 * r)

            # Step 1
            sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(s), eta)
            s_ = t_fn(sd)
            x_2 = (sigma_fn(s_) / sigma_fn(t)) * x - (t - s_).expm1() * denoised
            x_2 = x_2 + noise_sampler(sigma_fn(t), sigma_fn(s)) * s_noise * su
            denoised_2 = model(x_2, sigma_fn(s) * s_in, **extra_args)

            # Step 2
            sd, su = get_ancestral_step(sigma_fn(t), sigma_fn(t_next), eta)
            t_next_ = t_fn(sd)
            denoised_d = (1 - fac) * temp[0] + fac * temp[0]  # Use temp[0] instead of denoised
            x = denoised_2 + to_d(x, sigmas[i], denoised_d) * sd
            x = x + noise_sampler(sigma_fn(t), sigma_fn(t_next)) * s_noise * su
    return x

@torch.no_grad()
def sample_dpmpp_2m_cfg_pp(model, x, sigmas, extra_args=None, callback=None, disable=None):
    """DPM-Solver++(2M) with CFG++."""
    extra_args = {} if extra_args is None else extra_args
    
    temp = [0]
    def post_cfg_function(args):
        temp[0] = args["uncond_denoised"]
        return args["denoised"]
    
    model_options = extra_args.get("model_options", {}).copy()
    extra_args["model_options"] = ldm_patched.modules.model_patcher.set_model_options_post_cfg_function(model_options, post_cfg_function, disable_cfg1_optimization=True)
    
    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

    for i in trange(len(sigmas) - 1, disable=disable):
        denoised = 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 = denoised + to_d(x, sigmas[i], temp[0]) * sigmas[i + 1]
        else:
            h_last = t - t_fn(sigmas[i - 1])
            r = h_last / h
            denoised_d = (1 + 1 / (2 * r)) * temp[0] - (1 / (2 * r)) * old_denoised
            x = denoised + to_d(x, sigmas[i], denoised_d) * sigmas[i + 1]
        old_denoised = temp[0]
    return x

@torch.no_grad()
def sample_ode(model, x, sigmas, extra_args=None, callback=None, disable=None, solver="dopri5", rtol=1e-3, atol=1e-4, max_steps=250):
    """Implements ODE-based sampling."""
    sampler = ODESampler(solver, rtol, atol, max_steps)
    return sampler(model, x, sigmas, extra_args=extra_args, callback=callback, disable=disable)