ldm/models/diffusion/uni_pc/uni_pc.py

import torch
import torch.nn.functional as F
import math


class NoiseScheduleVP:
    def __init__(
        self,
        schedule="discrete",
        betas=None,
        alphas_cumprod=None,
        continuous_beta_0=0.1,
        continuous_beta_1=20.0,
    ):

        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 = 1.0
            self.t_array = torch.linspace(0.0, 1.0, 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 = 999.0
            self.cosine_t_max = (
                math.atan(self.cosine_beta_max * (1.0 + self.cosine_s) / math.pi)
                * 2.0
                * (1.0 + self.cosine_s)
                / math.pi
                - self.cosine_s
            )
            self.cosine_log_alpha_0 = math.log(math.cos(self.cosine_s / (1.0 + self.cosine_s) * math.pi / 2.0))
            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 = 1.0

    def marginal_log_mean_coeff(self, t):
        """
        Compute log(alpha_t) of a given continuous-time label t in [0, T].
        """
        if self.schedule == "discrete":
            return interpolate_fn(
                t.reshape((-1, 1)), self.t_array.to(t.device), self.log_alpha_array.to(t.device)
            ).reshape((-1))
        elif self.schedule == "linear":
            return -0.25 * t**2 * (self.beta_1 - self.beta_0) - 0.5 * t * self.beta_0
        elif self.schedule == "cosine":
            log_alpha_fn = lambda s: torch.log(torch.cos((s + self.cosine_s) / (1.0 + self.cosine_s) * math.pi / 2.0))
            log_alpha_t = log_alpha_fn(t) - self.cosine_log_alpha_0
            return log_alpha_t

    def marginal_alpha(self, t):
        """
        Compute alpha_t of a given continuous-time label t in [0, 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(1.0 - torch.exp(2.0 * 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(1.0 - torch.exp(2.0 * 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 = 2.0 * (self.beta_1 - self.beta_0) * torch.logaddexp(-2.0 * 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), -2.0 * lamb)
            t = interpolate_fn(
                log_alpha.reshape((-1, 1)),
                torch.flip(self.log_alpha_array.to(lamb.device), [1]),
                torch.flip(self.t_array.to(lamb.device), [1]),
            )
            return t.reshape((-1,))
        else:
            log_alpha = -0.5 * torch.logaddexp(-2.0 * lamb, torch.zeros((1,)).to(lamb))
            t_fn = (
                lambda log_alpha_t: torch.arccos(torch.exp(log_alpha_t + self.cosine_log_alpha_0))
                * 2.0
                * (1.0 + self.cosine_s)
                / math.pi
                - self.cosine_s
            )
            t = t_fn(log_alpha)
            return t


def model_wrapper(
    model,
    noise_schedule,
    model_type="noise",
    model_kwargs={},
    guidance_type="uncond",
    condition=None,
    unconditional_condition=None,
    guidance_scale=1.0,
    classifier_fn=None,
    classifier_kwargs={},
):

    def get_model_input_time(t_continuous):
        """
        Convert the continuous-time `t_continuous` (in [epsilon, T]) to the model input time.
        For discrete-time DPMs, we convert `t_continuous` in [1 / N, 1] to `t_input` in [0, 1000 * (N - 1) / N].
        For continuous-time DPMs, we just use `t_continuous`.
        """
        if noise_schedule.schedule == "discrete":
            return (t_continuous - 1.0 / noise_schedule.total_N) * 1000.0
        else:
            return t_continuous

    def noise_pred_fn(x, t_continuous, cond=None):
        if t_continuous.reshape((-1,)).shape[0] == 1:
            t_continuous = t_continuous.expand((x.shape[0]))
        t_input = get_model_input_time(t_continuous)
        if cond is None:
            output = model(x, t_input, None, **model_kwargs)
        else:
            output = model(x, t_input, cond, **model_kwargs)
        if model_type == "noise":
            return output
        elif model_type == "x_start":
            alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
            dims = x.dim()
            return (x - expand_dims(alpha_t, dims) * output) / expand_dims(sigma_t, dims)
        elif model_type == "v":
            alpha_t, sigma_t = noise_schedule.marginal_alpha(t_continuous), noise_schedule.marginal_std(t_continuous)
            dims = x.dim()
            return expand_dims(alpha_t, dims) * output + expand_dims(sigma_t, dims) * x
        elif model_type == "score":
            sigma_t = noise_schedule.marginal_std(t_continuous)
            dims = x.dim()
            return -expand_dims(sigma_t, dims) * output

    def cond_grad_fn(x, t_input):
        """
        Compute the gradient of the classifier, i.e. nabla_{x} log p_t(cond | x_t).
        """
        with torch.enable_grad():
            x_in = x.detach().requires_grad_(True)
            log_prob = classifier_fn(x_in, t_input, condition, **classifier_kwargs)
            return torch.autograd.grad(log_prob.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 = t_continuous.expand((x.shape[0]))
        if guidance_type == "uncond":
            return noise_pred_fn(x, t_continuous)
        elif guidance_type == "classifier":
            assert classifier_fn is not None
            t_input = get_model_input_time(t_continuous)
            cond_grad = cond_grad_fn(x, t_input)
            sigma_t = noise_schedule.marginal_std(t_continuous)
            noise = noise_pred_fn(x, t_continuous)
            return noise - guidance_scale * expand_dims(sigma_t, dims=cond_grad.dim()) * cond_grad
        elif guidance_type == "classifier-free":
            if guidance_scale == 1.0 or unconditional_condition is None:
                return noise_pred_fn(x, t_continuous, cond=condition)
            else:
                x_in = torch.cat([x] * 2)
                t_in = torch.cat([t_continuous] * 2)
                c_in = torch.cat([unconditional_condition, condition])
                noise_uncond, noise = noise_pred_fn(x_in, t_in, cond=c_in).chunk(2)
                return noise_uncond + guidance_scale * (noise - noise_uncond)

    assert model_type in ["noise", "x_start", "v"]
    assert guidance_type in ["uncond", "classifier", "classifier-free"]
    return model_fn


class UniPC:
    def __init__(self, model_fn, noise_schedule, predict_x0=True, thresholding=False, max_val=1.0, variant="bh1"):
        """Construct a UniPC.

        We support both data_prediction and noise_prediction.
        """
        self.model = model_fn
        self.noise_schedule = noise_schedule
        self.variant = variant
        self.predict_x0 = predict_x0
        self.thresholding = thresholding
        self.max_val = max_val

    def dynamic_thresholding_fn(self, x0, t=None):
        """
        The dynamic thresholding method.
        """
        dims = x0.dim()
        p = self.dynamic_thresholding_ratio
        s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
        s = expand_dims(torch.maximum(s, self.thresholding_max_val * torch.ones_like(s).to(s.device)), dims)
        x0 = torch.clamp(x0, -s, s) / s
        return x0

    def noise_prediction_fn(self, x, t):
        """
        Return the noise prediction model.
        """
        return self.model(x, t)

    def data_prediction_fn(self, x, t):
        """
        Return the data prediction model (with thresholding).
        """
        noise = self.noise_prediction_fn(x, t)
        dims = x.dim()
        alpha_t, sigma_t = self.noise_schedule.marginal_alpha(t), self.noise_schedule.marginal_std(t)
        x0 = (x - expand_dims(sigma_t, dims) * noise) / expand_dims(alpha_t, dims)
        if self.thresholding:
            p = 0.995  # A hyperparameter in the paper of "Imagen" [1].
            s = torch.quantile(torch.abs(x0).reshape((x0.shape[0], -1)), p, dim=1)
            s = expand_dims(torch.maximum(s, self.max_val * torch.ones_like(s).to(s.device)), dims)
            x0 = torch.clamp(x0, -s, s) / s
        return x0

    def model_fn(self, x, t):
        """
        Convert the model to the noise prediction model or the data prediction model.
        """
        if self.predict_x0:
            return self.data_prediction_fn(x, t)
        else:
            return self.noise_prediction_fn(x, t)

    def get_time_steps(self, skip_type, t_T, t_0, N, device):
        """Compute the intermediate time steps for sampling."""
        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)
            return self.noise_schedule.inverse_lambda(logSNR_steps)
        elif skip_type == "time_uniform":
            return torch.linspace(t_T, t_0, N + 1).to(device)
        elif skip_type == "time_quadratic":
            t_order = 2
            t = torch.linspace(t_T ** (1.0 / t_order), t_0 ** (1.0 / t_order), N + 1).pow(t_order).to(device)
            return t
        else:
            raise ValueError(
                "Unsupported skip_type {}, need to be 'logSNR' or 'time_uniform' or 'time_quadratic'".format(skip_type)
            )

    def multistep_uni_pc_update(self, x, model_prev_list, t_prev_list, t, t2, order, **kwargs):
        if len(t.shape) == 0:
            t = t.view(-1)
        if "bh" in self.variant:
            return self.multistep_uni_pc_bh_update(x, model_prev_list, t_prev_list, t, t2, order, **kwargs)
        

    def multistep_uni_pc_bh_update(self, x, model_prev_list, t_prev_list, t, t2, order, x_t=None, use_corrector=True):
        # print(f'using unified predictor-corrector with order {order} (solver type: B(h))')
        ns = self.noise_schedule
        assert order <= len(model_prev_list)
        dims = x.dim()

        # first compute rks
        t_prev_0 = t_prev_list[-1]
        lambda_prev_0 = ns.marginal_lambda(t_prev_0)
        lambda_t = ns.marginal_lambda(t)
        model_prev_0 = model_prev_list[-1]
        sigma_prev_0, sigma_t = ns.marginal_std(t_prev_0), ns.marginal_std(t)
        log_alpha_prev_0, log_alpha_t = ns.marginal_log_mean_coeff(t_prev_0), ns.marginal_log_mean_coeff(t)
        alpha_t = torch.exp(log_alpha_t)

        h = lambda_t - lambda_prev_0

        rks = []
        D1s = []
        for i in range(1, order):
            t_prev_i = t_prev_list[-(i + 1)]
            model_prev_i = model_prev_list[-(i + 1)]
            lambda_prev_i = ns.marginal_lambda(t_prev_i)
            rk = ((lambda_prev_i - lambda_prev_0) / h)[0]
            rks.append(rk)
            D1s.append((model_prev_i - model_prev_0) / rk)

        rks.append(1.0)
        rks = torch.tensor(rks, device=x.device)

        R = []
        b = []

        hh = -h[0] if self.predict_x0 else h[0]
        h_phi_1 = torch.expm1(hh)  # h\phi_1(h) = e^h - 1
        h_phi_k = h_phi_1 / hh - 1

        factorial_i = 1

        if self.variant == "bh1":
            B_h = hh
        elif self.variant == "bh2":
            B_h = torch.expm1(hh)
        else:
            raise NotImplementedError()

        for i in range(1, order + 1):
            R.append(torch.pow(rks, i - 1))
            b.append(h_phi_k * factorial_i / B_h)
            factorial_i *= i + 1
            h_phi_k = h_phi_k / hh - 1 / factorial_i

        R = torch.stack(R)
        b = torch.tensor(b, device=x.device)

        # now predictor
        use_predictor = len(D1s) > 0 and x_t is None
        if len(D1s) > 0:
            D1s = torch.stack(D1s, dim=1)  # (B, K)
            if x_t is None:
                # for order 2, we use a simplified version
                if order == 2:
                    rhos_p = torch.tensor([0.5], device=b.device)
                else:
                    rhos_p = torch.linalg.solve(R[:-1, :-1], b[:-1])
        else:
            D1s = None

        if use_corrector:
            # print('using corrector')
            # for order 1, we use a simplified version
            if order == 1:
                rhos_c = torch.tensor([0.5], device=b.device)
            else:
                rhos_c = torch.linalg.solve(R, b)

        model_t = None
        if self.predict_x0:
            x_t_ = expand_dims(sigma_t / sigma_prev_0, dims) * x - expand_dims(alpha_t * h_phi_1, dims) * model_prev_0

            if x_t is None:
                if use_predictor:
                    pred_res = torch.einsum("k,bkchw->bchw", rhos_p, D1s)
                else:
                    pred_res = 0
                x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * pred_res

            if use_corrector:
                model_t = self.model_fn(x_t, t2)
                if D1s is not None:
                    corr_res = torch.einsum("k,bkchw->bchw", rhos_c[:-1], D1s)
                else:
                    corr_res = 0
                D1_t = model_t - model_prev_0
                x_t = x_t_ - expand_dims(alpha_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
        else:
            x_t_ = (
                expand_dims(torch.exp(log_alpha_t - log_alpha_prev_0), dims) * x
                - expand_dims(sigma_t * h_phi_1, dims) * model_prev_0
            )
            if x_t is None:
                if use_predictor:
                    pred_res = torch.einsum("k,bkchw->bchw", rhos_p, D1s)
                else:
                    pred_res = 0
                x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * pred_res

            if use_corrector:
                model_t = self.model_fn(x_t, t2)
                if D1s is not None:
                    corr_res = torch.einsum("k,bkchw->bchw", rhos_c[:-1], D1s)
                else:
                    corr_res = 0
                D1_t = model_t - model_prev_0
                x_t = x_t_ - expand_dims(sigma_t * B_h, dims) * (corr_res + rhos_c[-1] * D1_t)
        return x_t, model_t


    def sample(
        self,
        x,
        steps=20,
        t_start=None,
        t_end=None,
        order=3,
        skip_type="time_uniform",
        method="singlestep",
        lower_order_final=True,
        denoise_to_zero=False,
        solver_type="dpm_solver",
        atol=0.0078,
        rtol=0.05,
        corrector=False,
        flags=None,
    ):
        
        device = x.device
        assert steps >= order
        with torch.no_grad():
            if flags.learn:
                load_from = f"{flags.log_path}/NFE-{steps}-256LSUN-uni_pc-{order}-decode/best.pt"
                timesteps = torch.load(load_from)['best_t_steps'].to(x.device)
                if flags.vs:
                    length = timesteps.shape[0] // 2
                    timesteps2 = timesteps[length:]
                    timesteps = timesteps[:length]
                else:
                    timesteps2 = timesteps   
            else: 
                t_0 = 1.0 / self.noise_schedule.total_N if t_end is None else t_end
                t_T = self.noise_schedule.T if t_start is None else t_start
                timesteps = self.get_time_steps(skip_type=skip_type, t_T=t_T, t_0=t_0, N=steps, device=device)
                timesteps2 = timesteps
                assert timesteps.shape[0] - 1 == steps
                
            def one_step(t1, t2, t_prev_list, model_prev_list, step, x_next, order, first=True, use_corrector=True):
                x_next, model_x_next = self.multistep_uni_pc_update(x_next, model_prev_list, t_prev_list, t1, t2, step, use_corrector=use_corrector)
                if model_x_next is None:
                    model_x_next = self.model_fn(x_next, t2)
                update_lists(t_prev_list, model_prev_list, t1, model_x_next, order, first=first)
                return x_next
            
            def update_lists(t_list, model_list, t_, model_x, order, first=False):
                if first:
                    t_list.append(t_)
                    model_list.append(model_x)
                    return
                for m in range(order - 1):
                    t_list[m] = t_list[m + 1]
                    model_list[m] = model_list[m + 1]
                t_list[-1] = t_
                model_list[-1] = model_x
                
            timesteps1 = timesteps 
            step = 0
            vec_t1 = timesteps1[0].expand((x.shape[0])) # bs
            vec_t2 = timesteps2[0].expand((x.shape[0])) # bs
            t_prev_list = [vec_t1]
            model_prev_list = [self.model_fn(x, vec_t2)]
            
            for step in range(1, order):
                vec_t1 = timesteps1[step].expand((x.shape[0]))
                vec_t2 = timesteps2[step].expand((x.shape[0]))
                x = one_step(vec_t1, vec_t2, t_prev_list, model_prev_list, step, x, order, first=True)
            
            for step in range(order, steps + 1):
                step_order = min(order, steps + 1 - step)
                vec_t1 = timesteps1[step].expand((x.shape[0]))
                vec_t2 = timesteps2[step].expand((x.shape[0]))
                use_corrector = True 
                if step == steps:
                    use_corrector = False
                x = one_step(vec_t1, vec_t2, t_prev_list, model_prev_list, step_order, x, order, first=False, use_corrector=use_corrector)
        return x


#############################################################
# other utility functions
#############################################################


def interpolate_fn(x, xp, yp):
    """
    A piecewise linear function y = f(x), using xp and yp as keypoints.
    We implement f(x) in a differentiable way (i.e. applicable for autograd).
    The function f(x) is well-defined for all x-axis. (For x beyond the bounds of xp, we use the outmost points of xp to define the linear function.)

    Args:
        x: PyTorch tensor with shape [N, C], where N is the batch size, C is the number of channels (we use C = 1 for DPM-Solver).
        xp: PyTorch tensor with shape [C, K], where K is the number of keypoints.
        yp: PyTorch tensor with shape [C, K].
    Returns:
        The function values f(x), with shape [N, C].
    """
    N, K = x.shape[0], xp.shape[1]
    all_x = torch.cat([x.unsqueeze(2), xp.unsqueeze(0).repeat((N, 1, 1))], dim=2)
    sorted_all_x, x_indices = torch.sort(all_x, 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, K),
            torch.tensor(K - 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_all_x, dim=2, index=start_idx.unsqueeze(2)).squeeze(2)
    end_x = torch.gather(sorted_all_x, 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, K),
            torch.tensor(K - 2, device=x.device),
            cand_start_idx,
        ),
    )
    y_positions_expanded = yp.unsqueeze(0).expand(N, -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


def expand_dims(v, dims):
    """
    Expand the tensor `v` to the dim `dims`.

    Args:
        `v`: a PyTorch tensor with shape [N].
        `dim`: a `int`.
    Returns:
        a PyTorch tensor with shape [N, 1, 1, ..., 1] and the total dimension is `dims`.
    """
    return v[(...,) + (None,) * (dims - 1)]