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unidiffuser-testing / dpm_solver_pp.py

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	import torch
	import torch.nn.functional as F
	import math
	import numpy as np
	import torch.distributed as dist


	def interpolate_fn(x: torch.Tensor, xp: torch.Tensor, yp: torch.Tensor) -> torch.Tensor:
	"""Performs piecewise linear interpolation for x, using xp and yp keypoints (knots).
	Performs separate interpolation for each channel.
	Args:
	x: [N, C] points to be calibrated (interpolated). Batch with C channels.
	xp: [C, K] x coordinates of the PWL knots. C is the number of channels, K is the number of knots.
	yp: [C, K] y coordinates of the PWL knots. C is the number of channels, K is the number of knots.
	Returns:
	Interpolated points of the shape [N, C].
	The piecewise linear function extends for the whole x axis (the outermost keypoints define the outermost
	infinite lines).
	For example:
	>>> calibrate1d(torch.tensor([[0.5]]), torch.tensor([[0.0, 1.0]]), torch.tensor([[0.0, 2.0]]))
	tensor([[1.0000]])
	>>> calibrate1d(torch.tensor([[-10]]), torch.tensor([[0.0, 1.0]]), torch.tensor([[0.0, 2.0]]))
	tensor([[-20.0000]])
	"""
	x_breakpoints = torch.cat([x.unsqueeze(2), xp.unsqueeze(0).repeat((x.shape[0], 1, 1))], dim=2)
	num_x_points = xp.shape[1]
	sorted_x_breakpoints, x_indices = torch.sort(x_breakpoints, dim=2)
	x_idx = torch.argmin(x_indices, dim=2)
	cand_start_idx = x_idx - 1
	start_idx = torch.where(
	torch.eq(x_idx, 0),
	torch.tensor(1, device=x.device),
	torch.where(
	torch.eq(x_idx, num_x_points), torch.tensor(num_x_points - 2, device=x.device), cand_start_idx,
	),
	)
	end_idx = torch.where(torch.eq(start_idx, cand_start_idx), start_idx + 2, start_idx + 1)
	start_x = torch.gather(sorted_x_breakpoints, dim=2, index=start_idx.unsqueeze(2)).squeeze(2)
	end_x = torch.gather(sorted_x_breakpoints, dim=2, index=end_idx.unsqueeze(2)).squeeze(2)
	start_idx2 = torch.where(
	torch.eq(x_idx, 0),
	torch.tensor(0, device=x.device),
	torch.where(
	torch.eq(x_idx, num_x_points), torch.tensor(num_x_points - 2, device=x.device), cand_start_idx,
	),
	)
	y_positions_expanded = yp.unsqueeze(0).expand(x.shape[0], -1, -1)
	start_y = torch.gather(y_positions_expanded, dim=2, index=start_idx2.unsqueeze(2)).squeeze(2)
	end_y = torch.gather(y_positions_expanded, dim=2, index=(start_idx2 + 1).unsqueeze(2)).squeeze(2)
	cand = start_y + (x - start_x) * (end_y - start_y) / (end_x - start_x)
	return cand


	class NoiseScheduleVP:
	def __init__(self, schedule='discrete', beta_0=1e-4, beta_1=2e-2, total_N=1000, betas=None, alphas_cumprod=None):
	"""Create a wrapper class for the forward SDE (VP type).

	The forward SDE ensures that the condition distribution q_{t\|0}(x_t \| x_0) = N ( alpha_t * x_0, sigma_t^2 * I ).
	We further define lambda_t = log(alpha_t) - log(sigma_t), which is the half-logSNR (described in the DPM-Solver paper).
	Therefore, we implement the functions for computing alpha_t, sigma_t and lambda_t. For t in [0, T], we have:

	log_alpha_t = self.marginal_log_mean_coeff(t)
	sigma_t = self.marginal_std(t)
	lambda_t = self.marginal_lambda(t)

	Moreover, as lambda(t) is an invertible function, we also support its inverse function:

	t = self.inverse_lambda(lambda_t)

	===============================================================

	We support two types of VPSDEs: linear (DDPM) and cosine (improved-DDPM). The hyperparameters for the noise
	schedule are the default settings in DDPM and improved-DDPM:

	beta_min: A `float` number. The smallest beta for the linear schedule.
	beta_max: A `float` number. The largest beta for the linear schedule.
	cosine_s: A `float` number. The hyperparameter in the cosine schedule.
	cosine_beta_max: A `float` number. The hyperparameter in the cosine schedule.
	T: A `float` number. The ending time of the forward process.

	Note that the original DDPM (linear schedule) used the discrete-time label (0 to 999). We convert the discrete-time
	label to the continuous-time time (followed Song et al., 2021), so the beta here is 1000x larger than those in DDPM.

	===============================================================

	Args:
	schedule: A `str`. The noise schedule of the forward SDE ('linear' or 'cosine').

	Returns:
	A wrapper object of the forward SDE (VP type).
	"""
	if schedule not in ['linear', 'discrete', 'cosine']:
	raise ValueError("Unsupported noise schedule {}. The schedule needs to be 'linear' or 'cosine'".format(schedule))
	self.total_N = total_N
	self.beta_0 = beta_0 * 1000.
	self.beta_1 = beta_1 * 1000.

	if schedule == 'discrete':
	if betas is not None:
	log_alphas = 0.5 * torch.log(1 - betas).cumsum(dim=0)
	else:
	assert alphas_cumprod is not None
	log_alphas = 0.5 * torch.log(alphas_cumprod)
	self.total_N = len(log_alphas)
	self.t_discrete = torch.linspace(1. / self.total_N, 1., self.total_N).reshape((1, -1))
	self.log_alpha_discrete = log_alphas.reshape((1, -1))

	self.cosine_s = 0.008
	self.cosine_beta_max = 999.
	self.cosine_t_max = math.atan(self.cosine_beta_max * (1. + self.cosine_s) / math.pi) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
	self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1. + self.cosine_s) * math.pi / 2.))
	self.schedule = schedule
	if schedule == 'cosine':
	# For the cosine schedule, T = 1 will have numerical issues. So we manually set the ending time T.
	# Note that T = 0.9946 may be not the optimal setting. However, we find it works well.
	self.T = 0.9946
	else:
	self.T = 1.

	def marginal_log_mean_coeff(self, t):
	"""
	Compute log(alpha_t) of a given continuous-time label t in [0, T].
	"""
	if self.schedule == 'linear':
	return -0.25 * t ** 2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
	elif self.schedule == 'discrete':
	return interpolate_fn(t.reshape((-1, 1)), self.t_discrete.clone().to(t.device), self.log_alpha_discrete.clone().to(t.device)).reshape((-1,))
	elif self.schedule == 'cosine':
	log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1. + self.cosine_s) * math.pi / 2.))
	log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0
	return log_alpha_t
	else:
	raise ValueError("Unsupported ")

	def marginal_alpha(self, t):
	return torch.exp(self.marginal_log_mean_coeff(t))

	def marginal_std(self, t):
	"""
	Compute sigma_t of a given continuous-time label t in [0, T].
	"""
	return torch.sqrt(1. - torch.exp(2. * self.marginal_log_mean_coeff(t)))

	def marginal_lambda(self, t):
	"""
	Compute lambda_t = log(alpha_t) - log(sigma_t) of a given continuous-time label t in [0, T].
	"""
	log_mean_coeff = self.marginal_log_mean_coeff(t)
	log_std = 0.5 * torch.log(1. - torch.exp(2. * log_mean_coeff))
	return log_mean_coeff - log_std

	def inverse_lambda(self, lamb):
	"""
	Compute the continuous-time label t in [0, T] of a given half-logSNR lambda_t.
	"""
	if self.schedule == 'linear':
	tmp = 2. * (self.beta_1 - self.beta_0) * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
	Delta = self.beta_0**2 + tmp
	return tmp / (torch.sqrt(Delta) + self.beta_0) / (self.beta_1 - self.beta_0)
	elif self.schedule == 'discrete':
	log_alpha = -0.5 * torch.logaddexp(torch.zeros((1,)).to(lamb.device), -2. * lamb)
	t = interpolate_fn(log_alpha.reshape((-1, 1)), torch.flip(self.log_alpha_discrete.clone().to(lamb.device), [1]), torch.flip(self.t_discrete.clone().to(lamb.device), [1]))
	return t.reshape((-1,))
	else:
	log_alpha = -0.5 * torch.logaddexp(-2. * lamb, torch.zeros((1,)).to(lamb))
	t_fn = lambda log_alpha_t: torch.arccos(torch.exp(log_alpha_t + self.cosine_log_alpha_0)) * 2. * (1. + self.cosine_s) / math.pi - self.cosine_s
	t = t_fn(log_alpha)
	return t


	def model_wrapper(model, noise_schedule=None, is_cond_classifier=False, classifier_fn=None, classifier_scale=1., time_input_type='1', total_N=1000, model_kwargs={}, is_deis=False):
	"""Create a wrapper function for the noise prediction model.

	DPM-Solver needs to solve the continuous-time diffusion ODEs. For DPMs trained on discrete-time labels, we need to
	firstly wrap the model function to a function that accepts the continuous time as the input.

	The input `model` has the following format:

	``
	model(x, t_input, **model_kwargs) -> noise
	``

	where `x` and `noise` have the same shape, and `t_input` is the time label of the model.
	(may be discrete-time labels (i.e. 0 to 999) or continuous-time labels (i.e. epsilon to T).)

	We wrap the model function to the following format:

	``
	def model_fn(x, t_continuous) -> noise:
	t_input = get_model_input_time(t_continuous)
	return model(x, t_input, **model_kwargs)
	``

	where `t_continuous` is the continuous time labels (i.e. epsilon to T). And we use `model_fn` for DPM-Solver.

	For DPMs with classifier guidance, we also combine the model output with the classifier gradient as used in [1].

	[1] P. Dhariwal and A. Q. Nichol, "Diffusion models beat GANs on image synthesis," in Advances in Neural
	Information Processing Systems, vol. 34, 2021, pp. 8780-8794.

	===============================================================

	Args:
	model: A noise prediction model with the following format:
	``
	def model(x, t_input, **model_kwargs):
	return noise
	``
	noise_schedule: A noise schedule object, such as NoiseScheduleVP. Only used for the classifier guidance.
	is_cond_classifier: A `bool`. Whether to use the classifier guidance.
	classifier_fn: A classifier function. Only used for the classifier guidance. The format is:
	``
	def classifier_fn(x, t_input):
	return logits
	``
	classifier_scale: A `float`. The scale for the classifier guidance.
	time_input_type: A `str`. The type for the time input of the model. We support three types:
	- '0': The continuous-time type. In this case, the model is trained on the continuous time,
	so `t_input` = `t_continuous`.
	- '1': The Type-1 discrete type described in the Appendix of DPM-Solver paper.
	For discrete-time DPMs, we recommend to use this type for DPM-Solver.
	- '2': The Type-2 discrete type described in the Appendix of DPM-Solver paper.
	total_N: A `int`. The total number of the discrete-time DPMs (default is 1000), used when `time_input_type`
	is '1' or '2'.
	model_kwargs: A `dict`. A dict for the other inputs of the model function.
	Returns:
	A function that accepts the continuous time as the input, with the following format:
	``
	def model_fn(x, t_continuous):
	t_input = get_model_input_time(t_continuous)
	return model(x, t_input, **model_kwargs)
	``
	"""
	def get_model_input_time(t_continuous):
	"""
	Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time.
	"""
	if time_input_type == '0':
	# discrete_type == '0' means that the model is continuous-time model.
	# For continuous-time DPMs, the continuous time equals to the discrete time.
	return t_continuous
	elif time_input_type == '1':
	# Type-1 discrete label, as detailed in the Appendix of DPM-Solver.
	return 1000. * torch.max(t_continuous - 1. / total_N, torch.zeros_like(t_continuous).to(t_continuous))
	elif time_input_type == '2':
	# Type-2 discrete label, as detailed in the Appendix of DPM-Solver.
	max_N = (total_N - 1) / total_N * 1000.
	return max_N * t_continuous
	else:
	raise ValueError("Unsupported time input type {}, must be '0' or '1' or '2'".format(time_input_type))

	def cond_fn(x, t_discrete, y):
	"""
	Compute the gradient of the classifier, multiplied with the sclae of the classifier guidance.
	"""
	assert y is not None
	with torch.enable_grad():
	x_in = x.detach().requires_grad_(True)
	logits = classifier_fn(x_in, t_discrete)
	log_probs = F.log_softmax(logits, dim=-1)
	selected = log_probs[range(len(logits)), y.view(-1)]
	return classifier_scale * torch.autograd.grad(selected.sum(), x_in)[0]

	def model_fn(x, t_continuous):
	"""
	The noise predicition model function that is used for DPM-Solver.
	"""
	if t_continuous.reshape((-1,)).shape[0] == 1:
	t_continuous = torch.ones((x.shape[0],)).to(x.device) * t_continuous
	if is_cond_classifier:
	y = model_kwargs.get("y", None)
	if y is None:
	raise ValueError("For classifier guidance, the label y has to be in the input.")
	t_discrete = get_model_input_time(t_continuous)
	noise_uncond = model(x, t_discrete, **model_kwargs)
	cond_grad = cond_fn(x, t_discrete, y)
	if is_deis:
	sigma_t = noise_schedule.marginal_std(t_continuous / 1000.)
	else:
	sigma_t = noise_schedule.marginal_std(t_continuous)
	dims = len(cond_grad.shape) - 1
	return noise_uncond - sigma_t[(...,) + (None,)dims] cond_grad
	else:
	t_discrete = get_model_input_time(t_continuous)
	return model(x, t_discrete, **model_kwargs)

	return model_fn


	class DPM_Solver:
	def __init__(self, model_fn, noise_schedule, predict_x0=False, thresholding=False, max_val=1.):
	"""Construct a DPM-Solver.

	Args:
	model_fn: A noise prediction model function which accepts the continuous-time input
	(t in [epsilon, T]):
	``
	def model_fn(x, t_continuous):
	return noise
	``
	noise_schedule: A noise schedule object, such as NoiseScheduleVP.
	"""
	self.model = model_fn
	self.noise_schedule = noise_schedule
	self.predict_x0 = predict_x0
	self.thresholding = thresholding
	self.max_val = max_val

	def model_fn(self, x, t):
	if self.predict_x0:
	alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t)
	noise = self.model(x, t)
	dims = len(x.shape) - 1
	x0 = (x - sigma_t[(...,) + (None,)dims] noise) / alpha_t[(...,) + (None,)*dims]
	if self.thresholding:
	p = 0.995
	s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
	s = torch.maximum(s, torch.ones_like(s).to(s.device))[(...,) + (None,)*dims]
	x0 = torch.clamp(x0, -s, s) / (s / self.max_val)
	return x0
	else:
	return self.model(x, t)

	def get_time_steps(self, skip_type, t_T, t_0, N, device):
	"""Compute the intermediate time steps for sampling.

	Args:
	skip_type: A `str`. The type for the spacing of the time steps. We support three types:
	- 'logSNR': uniform logSNR for the time steps, recommended for DPM-Solver.
	- 'time_uniform': uniform time for the time steps. (Used in DDIM and DDPM.)
	- 'time_quadratic': quadratic time for the time steps. (Used in DDIM for low-resolutional data.)
	t_T: A `float`. The starting time of the sampling (default is T).
	t_0: A `float`. The ending time of the sampling (default is epsilon).
	N: A `int`. The total number of the spacing of the time steps.
	device: A torch device.
	Returns:
	A pytorch tensor of the time steps, with the shape (N + 1,).
	"""
	if skip_type == 'logSNR':
	lambda_T = self.noise_schedule.marginal_lambda(torch.tensor(t_T).to(device))
	lambda_0 = self.noise_schedule.marginal_lambda(torch.tensor(t_0).to(device))
	logSNR_steps = torch.linspace(lambda_T.cpu().item(), lambda_0.cpu().item(), N + 1).to(device)
	# print(torch.min(torch.abs(logSNR_steps - self.noise_schedule.marginal_lambda(self.noise_schedule.inverse_lambda(logSNR_steps)))).item())
	return self.noise_schedule.inverse_lambda(logSNR_steps)
	elif skip_type == 't2':
	t_order = 2
	t = torch.linspace(t_T(1. / t_order), t_0(1. / t_order), N + 1).pow(t_order).to(device)
	return t
	elif skip_type == 'time_uniform':
	return torch.linspace(t_T, t_0, N + 1).to(device)
	elif skip_type == 'time_quadratic':
	t = torch.linspace(t_0, t_T, 10000000).to(device)
	quadratic_t = torch.sqrt(t)
	quadratic_steps = torch.linspace(quadratic_t[0], quadratic_t[-1], N + 1).to(device)
	return torch.flip(torch.cat([t[torch.searchsorted(quadratic_t, quadratic_steps)[:-1]], t_T * torch.ones((1,)).to(device)], dim=0), dims=[0])
	else:
	raise ValueError("Unsupported skip_type {}, need to be 'logSNR' or 'time_uniform' or 'time_quadratic'".format(skip_type))

	def get_time_steps_for_dpm_solver_fast(self, skip_type, t_T, t_0, steps, order, device):
	"""
	Compute the intermediate time steps and the order of each step for sampling by DPM-Solver-fast.

	We recommend DPM-Solver-fast for fast sampling of DPMs. Given a fixed number of function evaluations by `steps`,
	the sampling procedure by DPM-Solver-fast is:
	- Denote K = (steps // 3 + 1). We take K intermediate time steps for sampling.
	- If steps % 3 == 0, we use (K - 2) steps of DPM-Solver-3, and 1 step of DPM-Solver-2 and 1 step of DPM-Solver-1.
	- If steps % 3 == 1, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-1.
	- If steps % 3 == 2, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-2.

	============================================
	Args:
	t_T: A `float`. The starting time of the sampling (default is T).
	t_0: A `float`. The ending time of the sampling (default is epsilon).
	steps: A `int`. The total number of function evaluations (NFE).
	device: A torch device.
	Returns:
	orders: A list of the solver order of each step.
	timesteps: A pytorch tensor of the time steps, with the shape of (K + 1,).
	"""
	if order == 3:
	K = steps // 3 + 1
	if steps % 3 == 0:
	orders = [3,] * (K - 2) + [2, 1]
	elif steps % 3 == 1:
	orders = [3,] * (K - 1) + [1]
	else:
	orders = [3,] * (K - 1) + [2]
	timesteps = self.get_time_steps(skip_type, t_T, t_0, K, device)
	return orders, timesteps
	elif order == 2:
	K = steps // 2
	if steps % 2 == 0:
	orders = [2,] * K
	else:
	orders = [2,] * K + [1]
	timesteps = self.get_time_steps(skip_type, t_T, t_0, K, device)
	return orders, timesteps
	else:
	raise ValueError("order must >= 2")

	def denoise_fn(self, x, s, noise_s=None):
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	log_alpha_s = ns.marginal_log_mean_coeff(s)
	sigma_s = ns.marginal_std(s)

	if noise_s is None:
	noise_s = self.model_fn(x, s)
	x_0 = (
	(x - sigma_s[(...,) + (None,)dims] noise_s) / torch.exp(log_alpha_s)[(...,) + (None,)*dims]
	)
	return x_0

	def dpm_solver_first_update(self, x, s, t, noise_s=None, return_noise=False):
	"""
	A single step for DPM-Solver-1.

	Args:
	x: A pytorch tensor. The initial value at time `s`.
	s: A pytorch tensor. The starting time, with the shape (x.shape[0],).
	t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
	return_noise: A `bool`. If true, also return the predicted noise at time `s`.
	Returns:
	x_t: A pytorch tensor. The approximated solution at time `t`.
	"""
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t)
	h = lambda_t - lambda_s
	log_alpha_s, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(t)
	sigma_s, sigma_t = ns.marginal_std(s), ns.marginal_std(t)
	alpha_t = torch.exp(log_alpha_t)

	if self.predict_x0:
	phi_1 = (torch.exp(-h) - 1.) / (-1.)
	if noise_s is None:
	noise_s = self.model_fn(x, s)
	x_t = (
	(sigma_t / sigma_s)[(...,) + (None,)dims] x
	+ (alpha_t * phi_1)[(...,) + (None,)dims] noise_s
	)
	if return_noise:
	return x_t, {'noise_s': noise_s}
	else:
	return x_t
	else:
	phi_1 = torch.expm1(h)
	if noise_s is None:
	noise_s = self.model_fn(x, s)
	x_t = (
	torch.exp(log_alpha_t - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_t * phi_1)[(...,) + (None,)dims] noise_s
	)
	if return_noise:
	return x_t, {'noise_s': noise_s}
	else:
	return x_t

	def dpm_solver_second_update(self, x, s, t, r1=0.5, noise_s=None, return_noise=False, solver_type='dpm_solver'):
	"""
	A single step for DPM-Solver-2.

	Args:
	x: A pytorch tensor. The initial value at time `s`.
	s: A pytorch tensor. The starting time, with the shape (x.shape[0],).
	t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
	r1: A `float`. The hyperparameter of the second-order solver. We recommend the default setting `0.5`.
	noise_s: A pytorch tensor. The predicted noise at time `s`.
	If `noise_s` is None, we compute the predicted noise by `x` and `s`; otherwise we directly use it.
	return_noise: A `bool`. If true, also return the predicted noise at time `s` and `s1` (the intermediate time).
	Returns:
	x_t: A pytorch tensor. The approximated solution at time `t`.
	"""
	if r1 is None:
	r1 = 0.5
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t)
	h = lambda_t - lambda_s
	lambda_s1 = lambda_s + r1 * h
	s1 = ns.inverse_lambda(lambda_s1)
	log_alpha_s, log_alpha_s1, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(s1), ns.marginal_log_mean_coeff(t)
	sigma_s, sigma_s1, sigma_t = ns.marginal_std(s), ns.marginal_std(s1), ns.marginal_std(t)
	alpha_s1, alpha_t = torch.exp(log_alpha_s1), torch.exp(log_alpha_t)

	if self.predict_x0:
	phi_11 = torch.expm1(-r1 * h)
	phi_1 = torch.expm1(-h)

	if noise_s is None:
	noise_s = self.model_fn(x, s)
	x_s1 = (
	(sigma_s1 / sigma_s)[(...,) + (None,)dims] x
	- (alpha_s1 * phi_11)[(...,) + (None,)dims] noise_s
	)
	noise_s1 = self.model_fn(x_s1, s1)
	if solver_type == 'dpm_solver':
	x_t = (
	(sigma_t / sigma_s)[(...,) + (None,)dims] x
	- (alpha_t * phi_1)[(...,) + (None,)dims] noise_s
	- (0.5 / r1) * (alpha_t * phi_1)[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	elif solver_type == 'taylor':
	x_t = (
	(sigma_t / sigma_s)[(...,) + (None,)dims] x
	- (alpha_t * phi_1)[(...,) + (None,)dims] noise_s
	+ (1. / r1) * (alpha_t * ((torch.exp(-h) - 1.) / h + 1.))[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	else:
	raise ValueError("solver_type must be either dpm_solver or taylor, got {}".format(solver_type))
	else:
	phi_11 = torch.expm1(r1 * h)
	phi_1 = torch.expm1(h)

	if noise_s is None:
	noise_s = self.model_fn(x, s)
	x_s1 = (
	torch.exp(log_alpha_s1 - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_s1 * phi_11)[(...,) + (None,)dims] noise_s
	)
	noise_s1 = self.model_fn(x_s1, s1)
	if solver_type == 'dpm_solver':
	x_t = (
	torch.exp(log_alpha_t - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_t * phi_1)[(...,) + (None,)dims] noise_s
	- (0.5 / r1) * (sigma_t * phi_1)[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	elif solver_type == 'taylor':
	x_t = (
	torch.exp(log_alpha_t - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_t * phi_1)[(...,) + (None,)dims] noise_s
	- (1. / r1) * (sigma_t * ((torch.exp(h) - 1.) / h - 1.))[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	else:
	raise ValueError("solver_type must be either dpm_solver or taylor, got {}".format(solver_type))
	if return_noise:
	return x_t, {'noise_s': noise_s, 'noise_s1': noise_s1}
	else:
	return x_t


	def dpm_multistep_second_update(self, x, noise_prev_list, t_prev_list, t, solver_type="dpm_solver"):
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	noise_prev_1, noise_prev_0 = noise_prev_list
	t_prev_1, t_prev_0 = t_prev_list
	lambda_prev_1, lambda_prev_0, lambda_t = ns.marginal_lambda(t_prev_1), ns.marginal_lambda(t_prev_0), ns.marginal_lambda(t)
	log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
	sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
	alpha_t = torch.exp(log_alpha_t)

	h_0 = lambda_prev_0 - lambda_prev_1
	h = lambda_t - lambda_prev_0
	r0 = h_0 / h
	D1_0 = (1. / r0)[(...,) + (None,)dims] (noise_prev_0 - noise_prev_1)
	if self.predict_x0:
	if solver_type == 'taylor':
	x_t = (
	(sigma_t / sigma_prev_0)[(...,) + (None,)dims] x
	- (alpha_t * (torch.exp(-h) - 1.))[(...,) + (None,)dims] noise_prev_0
	+ (alpha_t * ((torch.exp(-h) - 1.) / h + 1.))[(...,) + (None,)dims] D1_0
	)
	elif solver_type == 'dpm_solver':
	x_t = (
	(sigma_t / sigma_prev_0)[(...,) + (None,)dims] x
	- (alpha_t * (torch.exp(-h) - 1.))[(...,) + (None,)dims] noise_prev_0
	- 0.5 * (alpha_t * (torch.exp(-h) - 1.))[(...,) + (None,)dims] D1_0
	)
	else:
	if solver_type == 'taylor':
	x_t = (
	torch.exp(log_alpha_t - log_alpha_prev_0)[(...,) + (None,)dims] x
	- (sigma_t * (torch.exp(h) - 1.))[(...,) + (None,)dims] noise_prev_0
	- (sigma_t * ((torch.exp(h) - 1.) / h - 1.))[(...,) + (None,)dims] D1_0
	)
	elif solver_type == 'dpm_solver':
	x_t = (
	torch.exp(log_alpha_t - log_alpha_prev_0)[(...,) + (None,)dims] x
	- (sigma_t * (torch.exp(h) - 1.))[(...,) + (None,)dims] noise_prev_0
	- 0.5 * (sigma_t * (torch.exp(h) - 1.))[(...,) + (None,)dims] D1_0
	)
	return x_t


	def dpm_multistep_third_update(self, x, noise_prev_list, t_prev_list, t, solver_type='dpm_solver'):
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	noise_prev_2, noise_prev_1, noise_prev_0 = noise_prev_list
	t_prev_2, t_prev_1, t_prev_0 = t_prev_list
	lambda_prev_2, lambda_prev_1, lambda_prev_0, lambda_t = ns.marginal_lambda(t_prev_2), ns.marginal_lambda(t_prev_1), ns.marginal_lambda(t_prev_0), ns.marginal_lambda(t)
	log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
	sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
	alpha_t = torch.exp(log_alpha_t)

	h_1 = lambda_prev_1 - lambda_prev_2
	h_0 = lambda_prev_0 - lambda_prev_1
	h = lambda_t - lambda_prev_0
	r0, r1 = h_0 / h, h_1 / h
	D1_0 = (1. / r0)[(...,) + (None,)dims] (noise_prev_0 - noise_prev_1)
	D1_1 = (1. / r1)[(...,) + (None,)dims] (noise_prev_1 - noise_prev_2)
	D1 = D1_0 + (r0 / (r0 + r1))[(...,) + (None,)dims] (D1_0 - D1_1)
	D2 = (1. / (r0 + r1))[(...,) + (None,)dims] (D1_0 - D1_1)
	if self.predict_x0:
	x_t = (
	(sigma_t / sigma_prev_0)[(...,) + (None,)dims] x
	- (alpha_t * (torch.exp(-h) - 1.))[(...,) + (None,)dims] noise_prev_0
	+ (alpha_t * ((torch.exp(-h) - 1.) / h + 1.))[(...,) + (None,)dims] D1
	- (alpha_t * ((torch.exp(-h) - 1. + h) / h*2 - 0.5))[(...,) + (None,)dims] * D2
	)
	else:
	x_t = (
	torch.exp(log_alpha_t - log_alpha_prev_0)[(...,) + (None,)dims] x
	- (sigma_t * (torch.exp(h) - 1.))[(...,) + (None,)dims] noise_prev_0
	- (sigma_t * ((torch.exp(h) - 1.) / h - 1.))[(...,) + (None,)dims] D1
	- (sigma_t * ((torch.exp(h) - 1. - h) / h*2 - 0.5))[(...,) + (None,)dims] * D2
	)
	return x_t

	def dpm_solver_third_update(self, x, s, t, r1=1./3., r2=2./3., noise_s=None, noise_s1=None, noise_s2=None, return_noise=False, solver_type='dpm_solver'):
	"""
	A single step for DPM-Solver-3.

	Args:
	x: A pytorch tensor. The initial value at time `s`.
	s: A pytorch tensor. The starting time, with the shape (x.shape[0],).
	t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
	r1: A `float`. The hyperparameter of the third-order solver. We recommend the default setting `1 / 3`.
	r2: A `float`. The hyperparameter of the third-order solver. We recommend the default setting `2 / 3`.
	noise_s: A pytorch tensor. The predicted noise at time `s`.
	If `noise_s` is None, we compute the predicted noise by `x` and `s`; otherwise we directly use it.
	noise_s1: A pytorch tensor. The predicted noise at time `s1` (the intermediate time given by `r1`).
	If `noise_s1` is None, we compute the predicted noise by `s1`; otherwise we directly use it.
	Returns:
	x_t: A pytorch tensor. The approximated solution at time `t`.
	"""
	if r1 is None:
	r1 = 1. / 3.
	if r2 is None:
	r2 = 2. / 3.
	ns = self.noise_schedule
	dims = len(x.shape) - 1
	lambda_s, lambda_t = ns.marginal_lambda(s), ns.marginal_lambda(t)
	h = lambda_t - lambda_s
	lambda_s1 = lambda_s + r1 * h
	lambda_s2 = lambda_s + r2 * h
	s1 = ns.inverse_lambda(lambda_s1)
	s2 = ns.inverse_lambda(lambda_s2)
	log_alpha_s, log_alpha_s1, log_alpha_s2, log_alpha_t = ns.marginal_log_mean_coeff(s), ns.marginal_log_mean_coeff(s1), ns.marginal_log_mean_coeff(s2), ns.marginal_log_mean_coeff(t)
	sigma_s, sigma_s1, sigma_s2, sigma_t = ns.marginal_std(s), ns.marginal_std(s1), ns.marginal_std(s2), ns.marginal_std(t)
	alpha_s1, alpha_s2, alpha_t = torch.exp(log_alpha_s1), torch.exp(log_alpha_s2), torch.exp(log_alpha_t)

	if self.predict_x0:
	phi_11 = torch.expm1(-r1 * h)
	phi_12 = torch.expm1(-r2 * h)
	phi_1 = torch.expm1(-h)
	phi_22 = torch.expm1(-r2 * h) / (r2 * h) + 1.
	phi_2 = phi_1 / h + 1.
	phi_3 = phi_2 / h - 0.5

	if noise_s is None:
	noise_s = self.model_fn(x, s)
	if noise_s1 is None:
	x_s1 = (
	(sigma_s1 / sigma_s)[(...,) + (None,)dims] x
	- (alpha_s1 * phi_11)[(...,) + (None,)dims] noise_s
	)
	noise_s1 = self.model_fn(x_s1, s1)
	if noise_s2 is None:
	x_s2 = (
	(sigma_s2 / sigma_s)[(...,) + (None,)dims] x
	- (alpha_s2 * phi_12)[(...,) + (None,)dims] noise_s
	+ r2 / r1 * (alpha_s2 * phi_22)[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	noise_s2 = self.model_fn(x_s2, s2)
	if solver_type == 'dpm_solver':
	x_t = (
	(sigma_t / sigma_s)[(...,) + (None,)dims] x
	- (alpha_t * phi_1)[(...,) + (None,)dims] noise_s
	+ (1. / r2) * (alpha_t * phi_2)[(...,) + (None,)dims] (noise_s2 - noise_s)
	)
	elif solver_type == 'taylor':
	D1_0 = (1. / r1) * (noise_s1 - noise_s)
	D1_1 = (1. / r2) * (noise_s2 - noise_s)
	D1 = (r2 * D1_0 - r1 * D1_1) / (r2 - r1)
	D2 = 2. * (D1_1 - D1_0) / (r2 - r1)
	x_t = (
	(sigma_t / sigma_s)[(...,) + (None,)dims] x
	- (alpha_t * phi_1)[(...,) + (None,)dims] noise_s
	+ (alpha_t * phi_2)[(...,) + (None,)dims] D1
	- (alpha_t * phi_3)[(...,) + (None,)dims] D2
	)
	else:
	raise ValueError("solver_type must be either dpm_solver or dpm_solver++, got {}".format(solver_type))
	else:
	phi_11 = torch.expm1(r1 * h)
	phi_12 = torch.expm1(r2 * h)
	phi_1 = torch.expm1(h)
	phi_22 = torch.expm1(r2 * h) / (r2 * h) - 1.
	phi_2 = phi_1 / h - 1.
	phi_3 = phi_2 / h - 0.5

	if noise_s is None:
	noise_s = self.model_fn(x, s)
	if noise_s1 is None:
	x_s1 = (
	torch.exp(log_alpha_s1 - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_s1 * phi_11)[(...,) + (None,)dims] noise_s
	)
	noise_s1 = self.model_fn(x_s1, s1)
	if noise_s2 is None:
	x_s2 = (
	torch.exp(log_alpha_s2 - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_s2 * phi_12)[(...,) + (None,)dims] noise_s
	- r2 / r1 * (sigma_s2 * phi_22)[(...,) + (None,)dims] (noise_s1 - noise_s)
	)
	noise_s2 = self.model_fn(x_s2, s2)
	if solver_type == 'dpm_solver':
	x_t = (
	torch.exp(log_alpha_t - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_t * phi_1)[(...,) + (None,)dims] noise_s
	- (1. / r2) * (sigma_t * phi_2)[(...,) + (None,)dims] (noise_s2 - noise_s)
	)
	elif solver_type == 'taylor':
	D1_0 = (1. / r1) * (noise_s1 - noise_s)
	D1_1 = (1. / r2) * (noise_s2 - noise_s)
	D1 = (r2 * D1_0 - r1 * D1_1) / (r2 - r1)
	D2 = 2. * (D1_1 - D1_0) / (r2 - r1)
	x_t = (
	torch.exp(log_alpha_t - log_alpha_s)[(...,) + (None,)dims] x
	- (sigma_t * phi_1)[(...,) + (None,)dims] noise_s
	- (sigma_t * phi_2)[(...,) + (None,)dims] D1
	- (sigma_t * phi_3)[(...,) + (None,)dims] D2
	)
	else:
	raise ValueError("solver_type must be either dpm_solver or dpm_solver++, got {}".format(solver_type))

	if return_noise:
	return x_t, {'noise_s': noise_s, 'noise_s1': noise_s1, 'noise_s2': noise_s2}
	else:
	return x_t

	def dpm_solver_update(self, x, s, t, order, return_noise=False, solver_type='dpm_solver', r1=None, r2=None):
	"""
	A single step for DPM-Solver of the given order `order`.

	Args:
	x: A pytorch tensor. The initial value at time `s`.
	s: A pytorch tensor. The starting time, with the shape (x.shape[0],).
	t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
	order: A `int`. The order of DPM-Solver. We only support order == 1 or 2 or 3.
	Returns:
	x_t: A pytorch tensor. The approximated solution at time `t`.
	"""
	if order == 1:
	return self.dpm_solver_first_update(x, s, t, return_noise=return_noise)
	elif order == 2:
	return self.dpm_solver_second_update(x, s, t, return_noise=return_noise, solver_type=solver_type, r1=r1)
	elif order == 3:
	return self.dpm_solver_third_update(x, s, t, return_noise=return_noise, solver_type=solver_type, r1=r1, r2=r2)
	else:
	raise ValueError("Solver order must be 1 or 2 or 3, got {}".format(order))

	def dpm_multistep_update(self, x, noise_prev_list, t_prev_list, t, order, solver_type='taylor'):
	"""
	A single step for DPM-Solver of the given order `order`.

	Args:
	x: A pytorch tensor. The initial value at time `s`.
	s: A pytorch tensor. The starting time, with the shape (x.shape[0],).
	t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
	order: A `int`. The order of DPM-Solver. We only support order == 1 or 2 or 3.
	Returns:
	x_t: A pytorch tensor. The approximated solution at time `t`.
	"""
	if order == 1:
	return self.dpm_solver_first_update(x, t_prev_list[-1], t, noise_s=noise_prev_list[-1])
	elif order == 2:
	return self.dpm_multistep_second_update(x, noise_prev_list, t_prev_list, t, solver_type=solver_type)
	elif order == 3:
	return self.dpm_multistep_third_update(x, noise_prev_list, t_prev_list, t, solver_type=solver_type)
	else:
	raise ValueError("Solver order must be 1 or 2 or 3, got {}".format(order))

	def dpm_solver_adaptive(self, x, order, t_T, t_0, h_init=0.05, atol=0.0078, rtol=0.05, theta=0.9, t_err=1e-5, solver_type='dpm_solver'):
	"""
	The adaptive step size solver based on DPM-Solver.

	Args:
	x: A pytorch tensor. The initial value at time `t_T`.
	order: A `int`. The (higher) order of the solver. We only support order == 2 or 3.
	t_T: A `float`. The starting time of the sampling (default is T).
	t_0: A `float`. The ending time of the sampling (default is epsilon).
	h_init: A `float`. The initial step size (for logSNR).
	atol: A `float`. The absolute tolerance of the solver. For image data, the default setting is 0.0078, followed [1].
	rtol: A `float`. The relative tolerance of the solver. The default setting is 0.05.
	theta: A `float`. The safety hyperparameter for adapting the step size. The default setting is 0.9, followed [1].
	t_err: A `float`. The tolerance for the time. We solve the diffusion ODE until the absolute error between the
	current time and `t_0` is less than `t_err`. The default setting is 1e-5.
	Returns:
	x_0: A pytorch tensor. The approximated solution at time `t_0`.

	[1] A. Jolicoeur-Martineau, K. Li, R. Piché-Taillefer, T. Kachman, and I. Mitliagkas, "Gotta go fast when generating data with score-based models," arXiv preprint arXiv:2105.14080, 2021.
	"""
	ns = self.noise_schedule
	s = t_T * torch.ones((x.shape[0],)).to(x)
	lambda_s = ns.marginal_lambda(s)
	lambda_0 = ns.marginal_lambda(t_0 * torch.ones_like(s).to(x))
	h = h_init * torch.ones_like(s).to(x)
	x_prev = x
	nfe = 0
	if order == 2:
	r1 = 0.5
	lower_update = lambda x, s, t: self.dpm_solver_first_update(x, s, t, return_noise=True)
	higher_update = lambda x, s, t, kwargs: self.dpm_solver_second_update(x, s, t, r1=r1, solver_type=solver_type, kwargs)
	elif order == 3:
	r1, r2 = 1. / 3., 2. / 3.
	lower_update = lambda x, s, t: self.dpm_solver_second_update(x, s, t, r1=r1, return_noise=True, solver_type=solver_type)
	higher_update = lambda x, s, t, kwargs: self.dpm_solver_third_update(x, s, t, r1=r1, r2=r2, solver_type=solver_type, kwargs)
	else:
	raise ValueError("For adaptive step size solver, order must be 2 or 3, got {}".format(order))
	while torch.abs((s - t_0)).mean() > t_err:
	t = ns.inverse_lambda(lambda_s + h)
	x_lower, lower_noise_kwargs = lower_update(x, s, t)
	x_higher = higher_update(x, s, t, **lower_noise_kwargs)
	delta = torch.max(torch.ones_like(x).to(x) * atol, rtol * torch.max(torch.abs(x_lower), torch.abs(x_prev)))
	norm_fn = lambda v: torch.sqrt(torch.square(v.reshape((v.shape[0], -1))).mean(dim=-1, keepdim=True))
	E = norm_fn((x_higher - x_lower) / delta).max()
	if torch.all(E <= 1.):
	x = x_higher
	s = t
	x_prev = x_lower
	lambda_s = ns.marginal_lambda(s)
	h = torch.min(theta * h * torch.float_power(E, -1. / order).float(), lambda_0 - lambda_s)
	nfe += order
	print('adaptive solver nfe', nfe)
	return x

	def sample(self, x, steps=10, eps=1e-4, T=None, order=3, skip_type='time_uniform',
	denoise=False, method='fast', solver_type='dpm_solver', atol=0.0078,
	rtol=0.05,
	):
	"""
	Compute the sample at time `eps` by DPM-Solver, given the initial `x` at time `T`.

	We support the following algorithms:

	- Adaptive step size DPM-Solver (i.e. DPM-Solver-12 and DPM-Solver-23)

	- Fixed order DPM-Solver (i.e. DPM-Solver-1, DPM-Solver-2 and DPM-Solver-3).

	- Fast version of DPM-Solver (i.e. DPM-Solver-fast), which uses uniform logSNR steps and combine
	different orders of DPM-Solver.

	We recommend DPM-Solver-fast for both fast sampling in few steps (<=20) and fast convergence in many steps (50 to 100).

	Choosing the algorithms:

	- If `adaptive_step_size` is True:
	We ignore `steps` and use adaptive step size DPM-Solver with a higher order of `order`.
	If `order`=2, we use DPM-Solver-12 which combines DPM-Solver-1 and DPM-Solver-2.
	If `order`=3, we use DPM-Solver-23 which combines DPM-Solver-2 and DPM-Solver-3.
	You can adjust the absolute tolerance `atol` and the relative tolerance `rtol` to balance the computatation costs
	(NFE) and the sample quality.

	- If `adaptive_step_size` is False and `fast_version` is True:
	We ignore `order` and use DPM-Solver-fast with number of function evaluations (NFE) = `steps`.
	We ignore `skip_type` and use uniform logSNR steps for DPM-Solver-fast.
	Given a fixed NFE=`steps`, the sampling procedure by DPM-Solver-fast is:
	- Denote K = (steps // 3 + 1). We take K intermediate time steps for sampling.
	- If steps % 3 == 0, we use (K - 2) steps of DPM-Solver-3, and 1 step of DPM-Solver-2 and 1 step of DPM-Solver-1.
	- If steps % 3 == 1, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-1.
	- If steps % 3 == 2, we use (K - 1) steps of DPM-Solver-3 and 1 step of DPM-Solver-2.

	- If `adaptive_step_size` is False and `fast_version` is False:
	We use DPM-Solver-`order` for `order`=1 or 2 or 3, with total [`steps` // `order`] * `order` NFE.
	We support three types of `skip_type`:
	- 'logSNR': uniform logSNR for the time steps, recommended for DPM-Solver.
	- 'time_uniform': uniform time for the time steps. (Used in DDIM and DDPM.)
	- 'time_quadratic': quadratic time for the time steps. (Used in DDIM.)

	=====================================================
	Args:
	x: A pytorch tensor. The initial value at time `T` (a sample from the normal distribution).
	steps: A `int`. The total number of function evaluations (NFE).
	eps: A `float`. The ending time of the sampling.
	We recommend `eps`=1e-3 when `steps` <= 15; and `eps`=1e-4 when `steps` > 15.
	T: A `float`. The starting time of the sampling. Default is `None`.
	If `T` is None, we use self.noise_schedule.T.
	order: A `int`. The order of DPM-Solver.
	skip_type: A `str`. The type for the spacing of the time steps. Default is 'logSNR'.
	adaptive_step_size: A `bool`. If true, use the adaptive step size DPM-Solver.
	fast_version: A `bool`. If true, use DPM-Solver-fast (recommended).
	atol: A `float`. The absolute tolerance of the adaptive step size solver.
	rtol: A `float`. The relative tolerance of the adaptive step size solver.
	Returns:
	x_0: A pytorch tensor. The approximated solution at time `t_0`.

	[1] A. Jolicoeur-Martineau, K. Li, R. Piché-Taillefer, T. Kachman, and I. Mitliagkas, "Gotta go fast when generating data with score-based models," arXiv preprint arXiv:2105.14080, 2021.
	"""
	t_0 = eps
	t_T = self.noise_schedule.T if T is None else T
	device = x.device
	if method == 'adaptive':
	with torch.no_grad():
	x = self.dpm_solver_adaptive(x, order=order, t_T=t_T, t_0=t_0, atol=atol, rtol=rtol, solver_type=solver_type)
	elif method == 'multistep':
	assert steps >= order
	if timesteps is None:
	timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
	assert timesteps.shape[0] - 1 == steps
	with torch.no_grad():
	vec_t = timesteps[0].expand((x.shape[0]))
	noise_prev_list = [self.model_fn(x, vec_t)]
	t_prev_list = [vec_t]
	for init_order in range(1, order):
	vec_t = timesteps[init_order].expand(x.shape[0])
	x = self.dpm_multistep_update(x, noise_prev_list, t_prev_list, vec_t, init_order, solver_type=solver_type)
	noise_prev_list.append(self.model_fn(x, vec_t))
	t_prev_list.append(vec_t)
	for step in range(order, steps + 1):
	vec_t = timesteps[step].expand(x.shape[0])
	x = self.dpm_multistep_update(x, noise_prev_list, t_prev_list, vec_t, order, solver_type=solver_type)
	for i in range(order - 1):
	t_prev_list[i] = t_prev_list[i + 1]
	noise_prev_list[i] = noise_prev_list[i + 1]
	t_prev_list[-1] = vec_t
	if step < steps:
	noise_prev_list[-1] = self.model_fn(x, vec_t)
	elif method == 'fast':
	orders, _ = self.get_time_steps_for_dpm_solver_fast(skip_type=skip_type, t_T=t_T, t_0=t_0, steps=steps, order=order, device=device)
	timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
	with torch.no_grad():
	i = 0
	for order in orders:
	vec_s, vec_t = torch.ones((x.shape[0],)).to(device) * timesteps[i], torch.ones((x.shape[0],)).to(device) * timesteps[i + order]
	h = self.noise_schedule.marginal_lambda(timesteps[i + order]) - self.noise_schedule.marginal_lambda(timesteps[i])
	r1 = None if order <= 1 else (self.noise_schedule.marginal_lambda(timesteps[i + 1]) - self.noise_schedule.marginal_lambda(timesteps[i])) / h
	r2 = None if order <= 2 else (self.noise_schedule.marginal_lambda(timesteps[i + 2]) - self.noise_schedule.marginal_lambda(timesteps[i])) / h
	x = self.dpm_solver_update(x, vec_s, vec_t, order, solver_type=solver_type, r1=r1, r2=r2)
	i += order
	elif method == 'singlestep':
	N_steps = steps // order
	orders = [order,] * N_steps
	timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=N_steps, device=device)
	assert len(timesteps) - 1 == N_steps
	with torch.no_grad():
	for i, order in enumerate(orders):
	vec_s, vec_t = torch.ones((x.shape[0],)).to(device) * timesteps[i], torch.ones((x.shape[0],)).to(device) * timesteps[i + 1]
	x = self.dpm_solver_update(x, vec_s, vec_t, order, solver_type=solver_type)
	if denoise:
	x = self.denoise_fn(x, torch.ones((x.shape[0],)).to(device) * t_0)
	return x