models/interpretable_diffusion/gaussian_diffusion.py

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

from torch import nn
from einops import reduce
from tqdm.auto import tqdm
from functools import partial
from .transformer import Transformer
from .model_utils import default, identity, extract


# gaussian diffusion trainer class


def linear_beta_schedule(timesteps):
    scale = 1000 / timesteps
    beta_start = scale * 0.0001
    beta_end = scale * 0.02
    return torch.linspace(beta_start, beta_end, timesteps, dtype=torch.float64)


def cosine_beta_schedule(timesteps, s=0.008):
    """

    cosine schedule

    as proposed in https://openreview.net/forum?id=-NEXDKk8gZ

    """
    steps = timesteps + 1
    x = torch.linspace(0, timesteps, steps, dtype=torch.float64)
    alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2
    alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
    betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
    return torch.clip(betas, 0, 0.999)


class Diffusion_TS(nn.Module):
    def __init__(

        self,

        seq_length,

        feature_size,

        n_layer_enc=3,

        n_layer_dec=6,

        d_model=None,

        timesteps=1000,

        sampling_timesteps=None,

        loss_type="l1",

        beta_schedule="cosine",

        n_heads=4,

        mlp_hidden_times=4,

        eta=0.0,

        attn_pd=0.0,

        resid_pd=0.0,

        kernel_size=None,

        padding_size=None,

        use_ff=True,

        reg_weight=None,

        **kwargs,

    ):
        super(Diffusion_TS, self).__init__()

        self.eta, self.use_ff = eta, use_ff
        self.seq_length = seq_length
        self.feature_size = feature_size
        self.ff_weight = default(reg_weight, math.sqrt(self.seq_length) / 5)

        self.model = Transformer(
            n_feat=feature_size,
            n_channel=seq_length,
            n_layer_enc=n_layer_enc,
            n_layer_dec=n_layer_dec,
            n_heads=n_heads,
            attn_pdrop=attn_pd,
            resid_pdrop=resid_pd,
            mlp_hidden_times=mlp_hidden_times,
            max_len=seq_length,
            n_embd=d_model,
            conv_params=[kernel_size, padding_size],
            **kwargs,
        )

        if beta_schedule == "linear":
            betas = linear_beta_schedule(timesteps)
        elif beta_schedule == "cosine":
            betas = cosine_beta_schedule(timesteps)
        else:
            raise ValueError(f"unknown beta schedule {beta_schedule}")

        alphas = 1.0 - betas
        alphas_cumprod = torch.cumprod(alphas, dim=0)
        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value=1.0)

        (timesteps,) = betas.shape
        self.num_timesteps = int(timesteps)
        self.loss_type = loss_type

        # sampling related parameters

        self.sampling_timesteps = default(
            sampling_timesteps, timesteps
        )  # default num sampling timesteps to number of timesteps at training

        assert self.sampling_timesteps <= timesteps
        self.fast_sampling = self.sampling_timesteps < timesteps

        # helper function to register buffer from float64 to float32

        register_buffer = lambda name, val: self.register_buffer(
            name, val.to(torch.float32)
        )

        register_buffer("betas", betas)
        register_buffer("alphas_cumprod", alphas_cumprod)
        register_buffer("alphas_cumprod_prev", alphas_cumprod_prev)

        # calculations for diffusion q(x_t | x_{t-1}) and others

        register_buffer("sqrt_alphas_cumprod", torch.sqrt(alphas_cumprod))
        register_buffer(
            "sqrt_one_minus_alphas_cumprod", torch.sqrt(1.0 - alphas_cumprod)
        )
        register_buffer("log_one_minus_alphas_cumprod", torch.log(1.0 - alphas_cumprod))
        register_buffer("sqrt_recip_alphas_cumprod", torch.sqrt(1.0 / alphas_cumprod))
        register_buffer(
            "sqrt_recipm1_alphas_cumprod", torch.sqrt(1.0 / alphas_cumprod - 1)
        )

        # calculations for posterior q(x_{t-1} | x_t, x_0)

        posterior_variance = (
            betas * (1.0 - alphas_cumprod_prev) / (1.0 - alphas_cumprod)
        )

        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)

        register_buffer("posterior_variance", posterior_variance)

        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain

        register_buffer(
            "posterior_log_variance_clipped",
            torch.log(posterior_variance.clamp(min=1e-20)),
        )
        register_buffer(
            "posterior_mean_coef1",
            betas * torch.sqrt(alphas_cumprod_prev) / (1.0 - alphas_cumprod),
        )
        register_buffer(
            "posterior_mean_coef2",
            (1.0 - alphas_cumprod_prev) * torch.sqrt(alphas) / (1.0 - alphas_cumprod),
        )

        # calculate reweighting

        register_buffer(
            "loss_weight",
            torch.sqrt(alphas) * torch.sqrt(1.0 - alphas_cumprod) / betas / 100,
        )

    def predict_noise_from_start(self, x_t, t, x0):
        return (
            extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x0
        ) / extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)

    def predict_start_from_noise(self, x_t, t, noise):
        return (
            extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t
            - extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise
        )

    def q_posterior(self, x_start, x_t, t):
        posterior_mean = (
            extract(self.posterior_mean_coef1, t, x_t.shape) * x_start
            + extract(self.posterior_mean_coef2, t, x_t.shape) * x_t
        )
        posterior_variance = extract(self.posterior_variance, t, x_t.shape)
        posterior_log_variance_clipped = extract(
            self.posterior_log_variance_clipped, t, x_t.shape
        )
        return posterior_mean, posterior_variance, posterior_log_variance_clipped

    def output(self, x, t, padding_masks=None):
        trend, season = self.model(x, t, padding_masks=padding_masks)
        model_output = trend + season
        return model_output

    def model_predictions(self, x, t, clip_x_start=False, padding_masks=None):
        if padding_masks is None:
            padding_masks = torch.ones(
                x.shape[0], self.seq_length, dtype=bool, device=x.device
            )

        maybe_clip = (
            partial(torch.clamp, min=-1.0, max=1.0) if clip_x_start else identity
        )
        x_start = self.output(x, t, padding_masks)
        x_start = maybe_clip(x_start)
        pred_noise = self.predict_noise_from_start(x, t, x_start)
        return pred_noise, x_start

    def p_mean_variance(self, x, t, clip_denoised=True):
        _, x_start = self.model_predictions(x, t)
        if clip_denoised:
            x_start.clamp_(-1.0, 1.0)
        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(
            x_start=x_start, x_t=x, t=t
        )
        return model_mean, posterior_variance, posterior_log_variance, x_start

    def p_sample(self, x, t: int, clip_denoised=True):
        batched_times = torch.full((x.shape[0],), t, device=x.device, dtype=torch.long)
        model_mean, _, model_log_variance, x_start = self.p_mean_variance(
            x=x, t=batched_times, clip_denoised=clip_denoised
        )
        noise = torch.randn_like(x) if t > 0 else 0.0  # no noise if t == 0
        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
        return pred_img, x_start

    @torch.no_grad()
    def sample(self, shape):
        device = self.betas.device
        img = torch.randn(shape, device=device)
        for t in tqdm(
            reversed(range(0, self.num_timesteps)),
            desc="sampling loop time step",
            total=self.num_timesteps,
        ):
            img, _ = self.p_sample(img, t)
        return img

    @torch.no_grad()
    def fast_sample(self, shape, clip_denoised=True):
        batch, device, total_timesteps, sampling_timesteps, eta = (
            shape[0],
            self.betas.device,
            self.num_timesteps,
            self.sampling_timesteps,
            self.eta,
        )

        # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)

        times = list(reversed(times.int().tolist()))
        time_pairs = list(
            zip(times[:-1], times[1:])
        )  # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
        img = torch.randn(shape, device=device)

        for time, time_next in tqdm(time_pairs, desc="sampling loop time step"):
            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
            pred_noise, x_start, *_ = self.model_predictions(
                img, time_cond, clip_x_start=clip_denoised
            )

            if time_next < 0:
                img = x_start
                continue

            alpha = self.alphas_cumprod[time]
            alpha_next = self.alphas_cumprod[time_next]
            sigma = (
                eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
            )
            c = (1 - alpha_next - sigma**2).sqrt()
            noise = torch.randn_like(img)
            img = x_start * alpha_next.sqrt() + c * pred_noise + sigma * noise

        return img

    def generate_mts(self, batch_size=16):
        feature_size, seq_length = self.feature_size, self.seq_length
        sample_fn = self.fast_sample if self.fast_sampling else self.sample
        return sample_fn((batch_size, seq_length, feature_size))

    @property
    def loss_fn(self):
        if self.loss_type == "l1":
            return F.l1_loss
        elif self.loss_type == "l2":
            return F.mse_loss
        else:
            raise ValueError(f"invalid loss type {self.loss_type}")

    def q_sample(self, x_start, t, noise=None):
        noise = default(noise, lambda: torch.randn_like(x_start))
        return (
            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
            + extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
        )

    def _train_loss(self, x_start, t, target=None, noise=None, padding_masks=None):
        noise = default(noise, lambda: torch.randn_like(x_start))
        if target is None:
            target = x_start

        x = self.q_sample(x_start=x_start, t=t, noise=noise)  # noise sample
        model_out = self.output(x, t, padding_masks)

        train_loss = self.loss_fn(model_out, target, reduction="none")

        fourier_loss = torch.tensor([0.0])
        if self.use_ff:
            fft1 = torch.fft.fft(model_out.transpose(1, 2), norm="forward")
            fft2 = torch.fft.fft(target.transpose(1, 2), norm="forward")
            fft1, fft2 = fft1.transpose(1, 2), fft2.transpose(1, 2)
            fourier_loss = self.loss_fn(
                torch.real(fft1), torch.real(fft2), reduction="none"
            ) + self.loss_fn(torch.imag(fft1), torch.imag(fft2), reduction="none")
            train_loss += self.ff_weight * fourier_loss

        train_loss = reduce(train_loss, "b ... -> b (...)", "mean")
        train_loss = train_loss * extract(self.loss_weight, t, train_loss.shape)
        return train_loss.mean()

    def forward(self, x, **kwargs):
        (
            b,
            c,
            n,
            device,
            feature_size,
        ) = (
            *x.shape,
            x.device,
            self.feature_size,
        )
        assert n == feature_size, f"number of variable must be {feature_size}"
        t = torch.randint(0, self.num_timesteps, (b,), device=device).long()
        return self._train_loss(x_start=x, t=t, **kwargs)

    def return_components(self, x, t: int):
        (
            b,
            c,
            n,
            device,
            feature_size,
        ) = (
            *x.shape,
            x.device,
            self.feature_size,
        )
        assert n == feature_size, f"number of variable must be {feature_size}"
        t = torch.tensor([t])
        t = t.repeat(b).to(device)
        x = self.q_sample(x, t)
        trend, season, residual = self.model(x, t, return_res=True)
        return trend, season, residual, x

    def fast_sample_infill(

        self,

        shape,

        target,

        sampling_timesteps,

        partial_mask=None,

        clip_denoised=True,

        model_kwargs=None,

    ):
        batch, device, total_timesteps, eta = (
            shape[0],
            self.betas.device,
            self.num_timesteps,
            self.eta,
        )

        # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)

        times = list(reversed(times.int().tolist()))
        time_pairs = list(
            zip(times[:-1], times[1:])
        )  # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
        img = torch.randn(shape, device=device)

        for time, time_next in tqdm(
            time_pairs, desc="conditional sampling loop time step"
        ):
            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
            pred_noise, x_start, *_ = self.model_predictions(
                img, time_cond, clip_x_start=clip_denoised
            )

            if time_next < 0:
                img = x_start
                continue

            alpha = self.alphas_cumprod[time]
            alpha_next = self.alphas_cumprod[time_next]
            sigma = (
                eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
            )
            c = (1 - alpha_next - sigma**2).sqrt()
            pred_mean = x_start * alpha_next.sqrt() + c * pred_noise
            noise = torch.randn_like(img)

            img = pred_mean + sigma * noise
            img = self.langevin_fn(
                sample=img,
                mean=pred_mean,
                sigma=sigma,
                t=time_cond,
                tgt_embs=target,
                partial_mask=partial_mask,
                **model_kwargs,
            )
            target_t = self.q_sample(target, t=time_cond)
            img[partial_mask] = target_t[partial_mask]

        img[partial_mask] = target[partial_mask]

        return img

    def sample_infill(

        self,

        shape,

        target,

        partial_mask=None,

        clip_denoised=True,

        model_kwargs=None,

    ):
        """

        Generate samples from the model and yield intermediate samples from

        each timestep of diffusion.

        """
        batch, device = shape[0], self.betas.device
        img = torch.randn(shape, device=device)
        for t in tqdm(
            reversed(range(0, self.num_timesteps)),
            desc="conditional sampling loop time step",
            total=self.num_timesteps,
        ):
            img = self.p_sample_infill(
                x=img,
                t=t,
                clip_denoised=clip_denoised,
                target=target,
                partial_mask=partial_mask,
                model_kwargs=model_kwargs,
            )

        img[partial_mask] = target[partial_mask]
        return img

    def p_sample_infill(

        self,

        x,

        target,

        t: int,

        partial_mask=None,

        clip_denoised=True,

        model_kwargs=None,

    ):
        b, *_, device = *x.shape, self.betas.device
        batched_times = torch.full((x.shape[0],), t, device=x.device, dtype=torch.long)
        model_mean, _, model_log_variance, _ = self.p_mean_variance(
            x=x, t=batched_times, clip_denoised=clip_denoised
        )
        noise = torch.randn_like(x) if t > 0 else 0.0  # no noise if t == 0
        sigma = (0.5 * model_log_variance).exp()
        pred_img = model_mean + sigma * noise

        pred_img = self.langevin_fn(
            sample=pred_img,
            mean=model_mean,
            sigma=sigma,
            t=batched_times,
            tgt_embs=target,
            partial_mask=partial_mask,
            **model_kwargs,
        )
        print(sigma.mean())
        target_t = self.q_sample(target, t=batched_times)
        pred_img[partial_mask] = target_t[partial_mask]

        return pred_img

    def langevin_fn(

        self,

        coef,

        partial_mask,

        tgt_embs,

        learning_rate,

        sample,

        mean,

        sigma,

        t,

        coef_=0.0,

        **kwargs,

    ):

        # we thus run more gradient updates at large diffusion step t to guide the generation then
        # reduce the number of gradient steps in stages to accelerate sampling.
        if t[0].item() < self.num_timesteps * 0.05:
            K = 0
        elif t[0].item() > self.num_timesteps * 0.9:
            K = 3
        elif t[0].item() > self.num_timesteps * 0.75:
            K = 2
            learning_rate = learning_rate * 0.5
        else:
            K = 1
            learning_rate = learning_rate * 0.25

        input_embs_param = torch.nn.Parameter(sample)

        with torch.enable_grad():
            for i in range(K):
                optimizer = torch.optim.Adagrad([input_embs_param], lr=learning_rate)
                optimizer.zero_grad()

                x_start = self.output(x=input_embs_param, t=t)

                if sigma.mean() == 0:
                    logp_term = (
                        coef * ((mean - input_embs_param) ** 2 / 1.0).mean(dim=0).sum()
                    )
                    infill_loss = (x_start[partial_mask] - tgt_embs[partial_mask]) ** 2
                    infill_loss = infill_loss.mean(dim=0).sum()
                else:
                    logp_term = (
                        coef
                        * ((mean - input_embs_param) ** 2 / sigma).mean(dim=0).sum()
                    )
                    infill_loss = (x_start[partial_mask] - tgt_embs[partial_mask]) ** 2
                    infill_loss = (infill_loss / sigma.mean()).mean(dim=0).sum()
                # 第二个等号后面最后一项消失了，因为当我们要求模型生成“狗”的图像时，扩散过程始终
                # 不变，对应的梯度也是0，可以抹掉。
                # https://lichtung612.github.io/posts/3-diffusion-models/
                # 第三个等号后面两项中，第一项是扩散模型本身的梯度引导，新增的只能是第二项，即classifier guidance只需要额外添加一个classifier的梯度来引导。
                if "auc_threshold" in kwargs:
                    auc_threshold = kwargs.get("auc_threshold")
                    auc_loss = compute_auc_loss(
                        input_embs_param, tgt_embs, auc_threshold
                    ) * (5 - K)
                else:
                    auc_loss = 0

                loss = logp_term + infill_loss + auc_loss
                print(logp_term, infill_loss, auc_loss)
                loss.backward()
                optimizer.step()

                # add more noise
                epsilon = torch.randn_like(input_embs_param.data)
                input_embs_param = torch.nn.Parameter(
                    (
                        input_embs_param.data + coef_ * sigma.mean().item() * epsilon
                    ).detach()
                )

        sample[~partial_mask] = input_embs_param.data[~partial_mask]
        return sample


import torch.nn.functional as F


def compute_auc_loss(predictions: torch.Tensor, targets=None, auc_threshold=None):
    # with torch.no_grad():
    #     if not auc_threshold:
    #         auc_target = torch.trapz(targets, dim=1).mean()
    # auc_prediction = torch.trapz(predictions, dim=1).mean()
    # l1 loss
    return (
        predictions[:, :, 0].sum(1) - auc_threshold
    ).mean()  # + F.l1_loss(predictions[:,:,0].sum(1), targets[:,:,0].sum(1)) * (targets[:,:,0].sum(1) - auc_threshold).mean()


def mse_with_auc(predictions, targets, auc_threshold=None, alpha=10.0):
    # Compute the mean squared error loss
    mse_loss = F.mse_loss(predictions, targets)

    # Compute the area under the curve (AUC) using the trapezoidal rule
    auc = torch.trapz(predictions, dim=1).mean()

    # Penalize if AUC exceeds the threshold
    auc_penalty = torch.abs(auc - auc_threshold)

    # Combine the losses
    total_loss = mse_loss + alpha * auc_penalty  # Adjust the penalty weight as needed
    return total_loss


if __name__ == "__main__":
    pass