from diffusers import DDIMScheduler
from diffusers.utils import BaseOutput
from diffusers.utils.torch_utils import randn_tensor
import torch
from typing import List, Optional, Tuple, Union
import numpy as np


class DDIMSchedulerOutput(BaseOutput):
    """
    Output class for the scheduler's `step` function output.

    Args:
        prev_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next model input in the
            denoising loop.
        pred_original_sample (`torch.FloatTensor` of shape `(batch_size, num_channels, height, width)` for images):
            The predicted denoised sample `(x_{0})` based on the model output from the current timestep.
            `pred_original_sample` can be used to preview progress or for guidance.
    """

    prev_sample: torch.FloatTensor
    pred_original_sample: Optional[torch.FloatTensor] = None


class MyDDIMScheduler(DDIMScheduler):

    def inv_step(
        self,
        model_output: torch.FloatTensor,
        timestep: int,
        sample: torch.FloatTensor,
        eta: float = 0.0,
        use_clipped_model_output: bool = False,
        generator=None,
        variance_noise: Optional[torch.FloatTensor] = None,
        return_dict: bool = True,
    ) -> Union[DDIMSchedulerOutput, Tuple]:
        """
        Predict the sample from the previous timestep by reversing the SDE. This function propagates the diffusion
        process from the learned model outputs (most often the predicted noise).

        Args:
            model_output (`torch.FloatTensor`):
                The direct output from learned diffusion model.
            timestep (`float`):
                The current discrete timestep in the diffusion chain.
            sample (`torch.FloatTensor`):
                A current instance of a sample created by the diffusion process.
            eta (`float`):
                The weight of noise for added noise in diffusion step.
            use_clipped_model_output (`bool`, defaults to `False`):
                If `True`, computes "corrected" `model_output` from the clipped predicted original sample. Necessary
                because predicted original sample is clipped to [-1, 1] when `self.config.clip_sample` is `True`. If no
                clipping has happened, "corrected" `model_output` would coincide with the one provided as input and
                `use_clipped_model_output` has no effect.
            generator (`torch.Generator`, *optional*):
                A random number generator.
            variance_noise (`torch.FloatTensor`):
                Alternative to generating noise with `generator` by directly providing the noise for the variance
                itself. Useful for methods such as [`CycleDiffusion`].
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] or `tuple`.

        Returns:
            [`~schedulers.scheduling_utils.DDIMSchedulerOutput`] or `tuple`:
                If return_dict is `True`, [`~schedulers.scheduling_ddim.DDIMSchedulerOutput`] is returned, otherwise a
                tuple is returned where the first element is the sample tensor.

        """
        if self.num_inference_steps is None:
            raise ValueError(
                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
            )

        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
        # Ideally, read DDIM paper in-detail understanding

        # Notation (<variable name> -> <name in paper>
        # - pred_noise_t -> e_theta(x_t, t)
        # - pred_original_sample -> f_theta(x_t, t) or x_0
        # - std_dev_t -> sigma_t
        # - eta -> η
        # - pred_sample_direction -> "direction pointing to x_t"
        # - pred_prev_sample -> "x_t-1"

        # 1. get previous step value (=t-1)
        prev_timestep = (
            timestep - self.config.num_train_timesteps // self.num_inference_steps
        )

        # 2. compute alphas, betas
        alpha_prod_t = self.alphas_cumprod[timestep]
        alpha_prod_t_prev = (
            self.alphas_cumprod[prev_timestep]
            if prev_timestep >= 0
            else self.final_alpha_cumprod
        )

        beta_prod_t = 1 - alpha_prod_t

        # 3. compute predicted original sample from predicted noise also called
        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        assert self.config.prediction_type == "epsilon"
        if self.config.prediction_type == "epsilon":
            pred_original_sample = (
                sample - beta_prod_t ** (0.5) * model_output
            ) / alpha_prod_t ** (0.5)
            pred_epsilon = model_output
        elif self.config.prediction_type == "sample":
            pred_original_sample = model_output
            pred_epsilon = (
                sample - alpha_prod_t ** (0.5) * pred_original_sample
            ) / beta_prod_t ** (0.5)
        elif self.config.prediction_type == "v_prediction":
            pred_original_sample = (alpha_prod_t**0.5) * sample - (
                beta_prod_t**0.5
            ) * model_output
            pred_epsilon = (alpha_prod_t**0.5) * model_output + (
                beta_prod_t**0.5
            ) * sample
        else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, `sample`, or"
                " `v_prediction`"
            )

        # 4. Clip or threshold "predicted x_0"
        if self.config.thresholding:
            pred_original_sample = self._threshold_sample(pred_original_sample)
        elif self.config.clip_sample:
            pred_original_sample = pred_original_sample.clamp(
                -self.config.clip_sample_range, self.config.clip_sample_range
            )

        # 5. compute variance: "sigma_t(η)" -> see formula (16)
        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
        variance = self._get_variance(timestep, prev_timestep)
        std_dev_t = eta * variance ** (0.5)

        if use_clipped_model_output:
            # the pred_epsilon is always re-derived from the clipped x_0 in Glide
            pred_epsilon = (
                sample - alpha_prod_t ** (0.5) * pred_original_sample
            ) / beta_prod_t ** (0.5)

        # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (
            0.5
        ) * pred_epsilon

        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
        # prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction

        prev_sample = (
            (alpha_prod_t ** (0.5) * sample) / alpha_prod_t_prev ** (0.5)
            + (alpha_prod_t_prev ** (0.5) * beta_prod_t ** (0.5) * model_output)
            / alpha_prod_t_prev ** (0.5)
            - (alpha_prod_t ** (0.5) * pred_sample_direction)
            / alpha_prod_t_prev ** (0.5)
        )

        if eta > 0:
            if variance_noise is not None and generator is not None:
                raise ValueError(
                    "Cannot pass both generator and variance_noise. Please make sure that either `generator` or"
                    " `variance_noise` stays `None`."
                )

            if variance_noise is None:
                variance_noise = randn_tensor(
                    model_output.shape,
                    generator=generator,
                    device=model_output.device,
                    dtype=model_output.dtype,
                )
            variance = std_dev_t * variance_noise

            prev_sample = prev_sample + variance

        if not return_dict:
            return (prev_sample,)

        return DDIMSchedulerOutput(
            prev_sample=prev_sample, pred_original_sample=pred_original_sample
        )
