def __init__(
            self,
            schedule='discrete',
            betas=None,
            alphas_cumprod=None,
            continuous_beta_0=0.1,
            continuous_beta_1=20.,
    ):
        """Create a wrapper class for the forward SDE (VP type).
        ***
        Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t.
                We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images.
        ***
        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 both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]).
        1. For discrete-time DPMs:
            For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by:
                t_i = (i + 1) / N
            e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1.
            We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3.
            Args:
                betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details)
                alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details)
            Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`.
            **Important**:  Please pay special attention for the args for `alphas_cumprod`:
                The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that
                    q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ).
                Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have
                    alpha_{t_n} = \sqrt{\hat{alpha_n}},
                and
                    log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}).
        2. For continuous-time DPMs:
            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:
            Args:
                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.
        ===============================================================
        Args:
            schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs,
                    'linear' or 'cosine' for continuous-time DPMs.
        Returns:
            A wrapper object of the forward SDE (VP type).

        ===============================================================
        Example:
        # For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1):
        >>> ns = NoiseScheduleVP('discrete', betas=betas)
        # For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1):
        >>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod)
        # For continuous-time DPMs (VPSDE), linear schedule:
        >>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.)
        """

        if schedule not in ['discrete', 'linear', 'cosine']:
            raise ValueError(
                "Unsupported noise schedule {}. The schedule needs to be 'discrete' or 'linear' or 'cosine'".format(
                    schedule))

        self.schedule = schedule
        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 = 1.
            self.t_array = torch.linspace(0., 1., self.total_N + 1)[1:].reshape((1, -1))
            self.log_alpha_array = log_alphas.reshape((1, -1,))
        else:
            self.total_N = 1000
            self.beta_0 = continuous_beta_0
            self.beta_1 = continuous_beta_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.
Create a wrapper class for the forward SDE (VP type).
        ***
        Update: We support discrete-time diffusion models by implementing a picewise linear interpolation for log_alpha_t.
                We recommend to use schedule='discrete' for the discrete-time diffusion models, especially for high-resolution images.
        ***
        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 both discrete-time DPMs (trained on n = 0, 1, ..., N-1) and continuous-time DPMs (trained on t in [t_0, T]).
        1. For discrete-time DPMs:
            For discrete-time DPMs trained on n = 0, 1, ..., N-1, we convert the discrete steps to continuous time steps by:
                t_i = (i + 1) / N
            e.g. for N = 1000, we have t_0 = 1e-3 and T = t_{N-1} = 1.
            We solve the corresponding diffusion ODE from time T = 1 to time t_0 = 1e-3.
            Args:
                betas: A `torch.Tensor`. The beta array for the discrete-time DPM. (See the original DDPM paper for details)
                alphas_cumprod: A `torch.Tensor`. The cumprod alphas for the discrete-time DPM. (See the original DDPM paper for details)
            Note that we always have alphas_cumprod = cumprod(betas). Therefore, we only need to set one of `betas` and `alphas_cumprod`.
            **Important**:  Please pay special attention for the args for `alphas_cumprod`:
                The `alphas_cumprod` is the \hat{alpha_n} arrays in the notations of DDPM. Specifically, DDPMs assume that
                    q_{t_n | 0}(x_{t_n} | x_0) = N ( \sqrt{\hat{alpha_n}} * x_0, (1 - \hat{alpha_n}) * I ).
                Therefore, the notation \hat{alpha_n} is different from the notation alpha_t in DPM-Solver. In fact, we have
                    alpha_{t_n} = \sqrt{\hat{alpha_n}},
                and
                    log(alpha_{t_n}) = 0.5 * log(\hat{alpha_n}).
        2. For continuous-time DPMs:
            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:
            Args:
                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.
        ===============================================================
        Args:
            schedule: A `str`. The noise schedule of the forward SDE. 'discrete' for discrete-time DPMs,
                    'linear' or 'cosine' for continuous-time DPMs.
        Returns:
            A wrapper object of the forward SDE (VP type).

        ===============================================================
        Example:
        # For discrete-time DPMs, given betas (the beta array for n = 0, 1, ..., N - 1):
        >>> ns = NoiseScheduleVP('discrete', betas=betas)
        # For discrete-time DPMs, given alphas_cumprod (the \hat{alpha_n} array for n = 0, 1, ..., N - 1):
        >>> ns = NoiseScheduleVP('discrete', alphas_cumprod=alphas_cumprod)
        # For continuous-time DPMs (VPSDE), linear schedule:
        >>> ns = NoiseScheduleVP('linear', continuous_beta_0=0.1, continuous_beta_1=20.)
        
ControlNet-v1-1-nightly/ldm/models/diffusion/dpm_solver/dpm_solver.py