0、快速访问

论文阅读笔记：Denoising Diffusion Implicit Models （1）
论文阅读笔记：Denoising Diffusion Implicit Models （2）
论文阅读笔记：Denoising Diffusion Implicit Models （3）
论文阅读笔记：Denoising Diffusion Implicit Models （4）

4、接上文[论文阅读笔记：论文阅读笔记：Denoising Diffusion Implicit Models （3）

5、代码

class DDIMPipeline(DiffusionPipeline):
    model_cpu_offload_seq = "unet"

    def __init__(self, unet, scheduler):
        super().__init__()

        # make sure scheduler can always be converted to DDIM
        scheduler = DDIMScheduler.from_config(scheduler.config)

        self.register_modules(unet=unet, scheduler=scheduler)

    @torch.no_grad()
    def __call__(
        self,
        batch_size: int = 1,
        generator: Optional[Union[torch.Generator, List[torch.Generator]]] = None,
        eta: float = 0.0,
        num_inference_steps: int = 50,
        use_clipped_model_output: Optional[bool] = None,
        output_type: Optional[str] = "pil",
        return_dict: bool = True,
    ) -> Union[ImagePipelineOutput, Tuple]:

        # Sample gaussian noise to begin loop
        if isinstance(self.unet.config.sample_size, int):
            image_shape = (
                batch_size,
                self.unet.config.in_channels,
                self.unet.config.sample_size,
                self.unet.config.sample_size,
            )
        else:
            image_shape = (batch_size, self.unet.config.in_channels, *self.unet.config.sample_size)

        if isinstance(generator, list) and len(generator) != batch_size:
            raise ValueError(
                f"You have passed a list of generators of length {len(generator)}, but requested an effective batch"
                f" size of {batch_size}. Make sure the batch size matches the length of the generators."
            )
		# 随即生成噪音
        image = randn_tensor(image_shape, generator=generator, device=self._execution_device, dtype=self.unet.dtype)

        # 设置步数间隔。例如num_inference_steps = 50,然而总步长为1000,那么就是每次跳20步，例如在当前时刻， timestep=980, prev_timestep=960
        self.scheduler.set_timesteps(num_inference_steps)

        for t in self.progress_bar(self.scheduler.timesteps):
            # 1. 预测出timestep=980时刻对应噪音
            model_output = self.unet(image, t).sample

            # 2. 调用scheduler的方法step，执行公式（）得到prev_timestep=960时刻的图像
            image = self.scheduler.step(
                model_output, t, image, eta=eta, use_clipped_model_output=use_clipped_model_output, generator=generator
            ).prev_sample

        image = (image / 2 + 0.5).clamp(0, 1)
        image = image.cpu().permute(0, 2, 3, 1).numpy()
        if output_type == "pil":
            image = self.numpy_to_pil(image)

        if not return_dict:
            return (image,)

        return ImagePipelineOutput(images=image)
 
 class DDIMScheduler(SchedulerMixin, ConfigMixin):
    _compatibles = [e.name for e in KarrasDiffusionSchedulers]
    order = 1

    @register_to_config
    def __init__(
        self,
        num_train_timesteps: int = 1000,
        beta_start: float = 0.0001,
        beta_end: float = 0.02,
        beta_schedule: str = "linear",
        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
        clip_sample: bool = True,
        set_alpha_to_one: bool = True,
        steps_offset: int = 0,
        prediction_type: str = "epsilon",
        thresholding: bool = False,
        dynamic_thresholding_ratio: float = 0.995,
        clip_sample_range: float = 1.0,
        sample_max_value: float = 1.0,
        timestep_spacing: str = "leading",
        rescale_betas_zero_snr: bool = False,
    ):
        if trained_betas is not None:
            self.betas = torch.tensor(trained_betas, dtype=torch.float32)
        elif beta_schedule == "linear":
            self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
        elif beta_schedule == "scaled_linear":
            # this schedule is very specific to the latent diffusion model.
            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
        elif beta_schedule == "squaredcos_cap_v2":
            # Glide cosine schedule
            self.betas = betas_for_alpha_bar(num_train_timesteps)
        else:
            raise NotImplementedError(f"{beta_schedule} is not implemented for {self.__class__}")

        # Rescale for zero SNR
        if rescale_betas_zero_snr:
            self.betas = rescale_zero_terminal_snr(self.betas)

        self.alphas = 1.0 - self.betas
        self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)

        # At every step in ddim, we are looking into the previous alphas_cumprod
        # For the final step, there is no previous alphas_cumprod because we are already at 0
        # `set_alpha_to_one` decides whether we set this parameter simply to one or
        # whether we use the final alpha of the "non-previous" one.
        self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]

        # standard deviation of the initial noise distribution
        self.init_noise_sigma = 1.0

        # setable values
        self.num_inference_steps = None
        self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy().astype(np.int64))

    def scale_model_input(self, sample: torch.Tensor, timestep: Optional[int] = None) -> torch.Tensor:
        """
        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
        current timestep.

        Args:
            sample (`torch.Tensor`):
                The input sample.
            timestep (`int`, *optional*):
                The current timestep in the diffusion chain.

        Returns:
            `torch.Tensor`:
                A scaled input sample.
        """
        return sample

    def _get_variance(self, timestep, prev_timestep):
        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
        beta_prod_t_prev = 1 - alpha_prod_t_prev

        variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)

        return variance

    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler._threshold_sample
    def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
        """
        "Dynamic thresholding: At each sampling step we set s to a certain percentile absolute pixel value in xt0 (the
        prediction of x_0 at timestep t), and if s > 1, then we threshold xt0 to the range [-s, s] and then divide by
        s. Dynamic thresholding pushes saturated pixels (those near -1 and 1) inwards, thereby actively preventing
        pixels from saturation at each step. We find that dynamic thresholding results in significantly better
        photorealism as well as better image-text alignment, especially when using very large guidance weights."

        https://arxiv.org/abs/2205.11487
        """
        dtype = sample.dtype
        batch_size, channels, *remaining_dims = sample.shape

        if dtype not in (torch.float32, torch.float64):
            sample = sample.float()  # upcast for quantile calculation, and clamp not implemented for cpu half

        # Flatten sample for doing quantile calculation along each image
        sample = sample.reshape(batch_size, channels * np.prod(remaining_dims))

        abs_sample = sample.abs()  # "a certain percentile absolute pixel value"

        s = torch.quantile(abs_sample, self.config.dynamic_thresholding_ratio, dim=1)
        s = torch.clamp(
            s, min=1, max=self.config.sample_max_value
        )  # When clamped to min=1, equivalent to standard clipping to [-1, 1]
        s = s.unsqueeze(1)  # (batch_size, 1) because clamp will broadcast along dim=0
        sample = torch.clamp(sample, -s, s) / s  # "we threshold xt0 to the range [-s, s] and then divide by s"

        sample = sample.reshape(batch_size, channels, *remaining_dims)
        sample = sample.to(dtype)

        return sample

    def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
        """
        Sets the discrete timesteps used for the diffusion chain (to be run before inference).

        Args:
            num_inference_steps (`int`):
                The number of diffusion steps used when generating samples with a pre-trained model.
        """

        if num_inference_steps > self.config.num_train_timesteps:
            raise ValueError(
                f"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
                f" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
                f" maximal {self.config.num_train_timesteps} timesteps."
            )

        self.num_inference_steps = num_inference_steps

        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
        if self.config.timestep_spacing == "linspace":
            timesteps = (
                np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps)
                .round()[::-1]
                .copy()
                .astype(np.int64)
            )
        elif self.config.timestep_spacing == "leading":
            step_ratio = self.config.num_train_timesteps // self.num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.int64)
            timesteps += self.config.steps_offset
        elif self.config.timestep_spacing == "trailing":
            step_ratio = self.config.num_train_timesteps / self.num_inference_steps
            # creates integer timesteps by multiplying by ratio
            # casting to int to avoid issues when num_inference_step is power of 3
            timesteps = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)).astype(np.int64)
            timesteps -= 1
        else:
            raise ValueError(
                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'."
            )

        self.timesteps = torch.from_numpy(timesteps).to(device)

    def step(
        self,
        model_output: torch.Tensor,
        timestep: int,
        sample: torch.Tensor,
        eta: float = 0.0,
        use_clipped_model_output: bool = False,
        generator=None,
        variance_noise: Optional[torch.Tensor] = None,
        return_dict: bool = True,
    ) -> Union[DDIMSchedulerOutput, Tuple]:
        
        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"
            )

        # 1. get previous step value (=t-1)；
        # timestep=980，self.config.num_train_timesteps=1000, self.num_inference_steps=50
        # prev_timestep = 960，步数的跳跃间隔为20
        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
        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

        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,
                pred_original_sample,
            )

        return DDIMSchedulerOutput(prev_sample=prev_sample, pred_original_sample=pred_original_sample)

    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.add_noise
    def add_noise(
        self,
        original_samples: torch.Tensor,
        noise: torch.Tensor,
        timesteps: torch.IntTensor,
    ) -> torch.Tensor:
        # Make sure alphas_cumprod and timestep have same device and dtype as original_samples
        # Move the self.alphas_cumprod to device to avoid redundant CPU to GPU data movement
        # for the subsequent add_noise calls
        self.alphas_cumprod = self.alphas_cumprod.to(device=original_samples.device)
        alphas_cumprod = self.alphas_cumprod.to(dtype=original_samples.dtype)
        timesteps = timesteps.to(original_samples.device)

        sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
        while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)

        sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(original_samples.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
        return noisy_samples

    # Copied from diffusers.schedulers.scheduling_ddpm.DDPMScheduler.get_velocity
    def get_velocity(self, sample: torch.Tensor, noise: torch.Tensor, timesteps: torch.IntTensor) -> torch.Tensor:
        # Make sure alphas_cumprod and timestep have same device and dtype as sample
        self.alphas_cumprod = self.alphas_cumprod.to(device=sample.device)
        alphas_cumprod = self.alphas_cumprod.to(dtype=sample.dtype)
        timesteps = timesteps.to(sample.device)

        sqrt_alpha_prod = alphas_cumprod[timesteps] ** 0.5
        sqrt_alpha_prod = sqrt_alpha_prod.flatten()
        while len(sqrt_alpha_prod.shape) < len(sample.shape):
            sqrt_alpha_prod = sqrt_alpha_prod.unsqueeze(-1)

        sqrt_one_minus_alpha_prod = (1 - alphas_cumprod[timesteps]) ** 0.5
        sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.flatten()
        while len(sqrt_one_minus_alpha_prod.shape) < len(sample.shape):
            sqrt_one_minus_alpha_prod = sqrt_one_minus_alpha_prod.unsqueeze(-1)

        velocity = sqrt_alpha_prod * noise - sqrt_one_minus_alpha_prod * sample
        return velocity

    def __len__(self):
        return self.config.num_train_timesteps