def multistep_dpm_solver_second_update(self, x, model_prev_list, t_prev_list, t, solver_type="dpm_solver"):
        """
        Multistep solver DPM-Solver-2 from time `t_prev_list[-1]` to time `t`.
        Args:
            x: A pytorch tensor. The initial value at time `s`.
            model_prev_list: A list of pytorch tensor. The previous computed model values.
            t_prev_list: A list of pytorch tensor. The previous times, each time has the shape (x.shape[0],)
            t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
            solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers.
                The type slightly impacts the performance. We recommend to use 'dpm_solver' type.
        Returns:
            x_t: A pytorch tensor. The approximated solution at time `t`.
        """
        if solver_type not in ['dpm_solver', 'taylor']:
            raise ValueError("'solver_type' must be either 'dpm_solver' or 'taylor', got {}".format(solver_type))
        ns = self.noise_schedule
        dims = x.dim()
        model_prev_1, model_prev_0 = model_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 = expand_dims(1. / r0, dims) * (model_prev_0 - model_prev_1)
        if self.predict_x0:
            if solver_type == 'dpm_solver':
                x_t = (
                        expand_dims(sigma_t / sigma_prev_0, dims) * x
                        - expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * model_prev_0
                        - 0.5 * expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * D1_0
                )
            elif solver_type == 'taylor':
                x_t = (
                        expand_dims(sigma_t / sigma_prev_0, dims) * x
                        - expand_dims(alpha_t * (torch.exp(-h) - 1.), dims) * model_prev_0
                        + expand_dims(alpha_t * ((torch.exp(-h) - 1.) / h + 1.), dims) * D1_0
                )
        else:
            if solver_type == 'dpm_solver':
                x_t = (
                        expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x
                        - expand_dims(sigma_t * (torch.exp(h) - 1.), dims) * model_prev_0
                        - 0.5 * expand_dims(sigma_t * (torch.exp(h) - 1.), dims) * D1_0
                )
            elif solver_type == 'taylor':
                x_t = (
                        expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x
                        - expand_dims(sigma_t * (torch.exp(h) - 1.), dims) * model_prev_0
                        - expand_dims(sigma_t * ((torch.exp(h) - 1.) / h - 1.), dims) * D1_0
                )
        return x_t

        Multistep solver DPM-Solver-2 from time `t_prev_list[-1]` to time `t`.
        Args:
            x: A pytorch tensor. The initial value at time `s`.
            model_prev_list: A list of pytorch tensor. The previous computed model values.
            t_prev_list: A list of pytorch tensor. The previous times, each time has the shape (x.shape[0],)
            t: A pytorch tensor. The ending time, with the shape (x.shape[0],).
            solver_type: either 'dpm_solver' or 'taylor'. The type for the high-order solvers.
                The type slightly impacts the performance. We recommend to use 'dpm_solver' type.
        Returns:
            x_t: A pytorch tensor. The approximated solution at time `t`.
        
ldm/models/diffusion/dpm_solver/dpm_solver.py