motionpaint.py

### this file contains MotionPaint pipeline, modified from Stable Video Diffusion pipeline.

from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL.Image
import torch
import torch.nn.functional as F
from transformers import CLIPImageProcessor, CLIPVisionModelWithProjection

from diffusers.image_processor import VaeImageProcessor
from diffusers.models import AutoencoderKLTemporalDecoder, UNetSpatioTemporalConditionModel
from diffusers.schedulers import EulerDiscreteScheduler
from diffusers.utils import PIL_INTERPOLATION, BaseOutput, logging
from diffusers.utils.torch_utils import randn_tensor
from diffusers.pipelines.pipeline_utils import DiffusionPipeline
 
logger = logging.get_logger(__name__)  # pylint: disable=invalid-name

class CrossAttnStoreProcessor:
    def __init__(self):
        self.attention_probs = None

    def __call__(
        self,
        attn,
        hidden_states,
        encoder_hidden_states=None,
        attention_mask=None,
    ):
        batch_size, sequence_length, _ = hidden_states.shape
        attention_mask = attn.prepare_attention_mask(attention_mask, sequence_length, batch_size)
        query = attn.to_q(hidden_states)

        if encoder_hidden_states is None:
            encoder_hidden_states = hidden_states
        elif attn.norm_cross:
            encoder_hidden_states = attn.norm_encoder_hidden_states(encoder_hidden_states)

        key = attn.to_k(encoder_hidden_states)
        value = attn.to_v(encoder_hidden_states)

        query = attn.head_to_batch_dim(query)
        key = attn.head_to_batch_dim(key)
        value = attn.head_to_batch_dim(value)

        self.attention_probs = attn.get_attention_scores(query, key, attention_mask)
        hidden_states = torch.bmm(self.attention_probs, value)
        hidden_states = attn.batch_to_head_dim(hidden_states)

        # linear proj
        hidden_states = attn.to_out[0](hidden_states)
        # dropout
        hidden_states = attn.to_out[1](hidden_states)

        return hidden_states
        
def preprocess_image(image, batch_size):
    w, h = image.size
    w, h = (x - x % 8 for x in (w, h))  # resize to integer multiple of 8
    image = image.resize((w, h), resample=PIL_INTERPOLATION["lanczos"])
    image = np.array(image).astype(np.float32) / 255.0
    image = np.vstack([image[None].transpose(0, 3, 1, 2)] * batch_size)
    image = torch.from_numpy(image)
    return 2.0 * image - 1.0


def preprocess_mask(mask, batch_size, num_frames, scale_factor=8):
    if not isinstance(mask, torch.FloatTensor):
        mask = mask.convert("L")
        w, h = mask.size
        w, h = (x - x % 8 for x in (w, h))  # resize to integer multiple of 8
        mask = mask.resize((w // scale_factor, h // scale_factor),
                           resample=PIL_INTERPOLATION["lanczos"])

        mask = np.array(mask).astype(np.float32) / 255.0
        mask = np.where(mask > 0.5, 1.0, 0.0)
        mask = np.tile(mask, (4, 1, 1))
        mask = np.vstack([mask[None]] * num_frames)
        mask = np.vstack([mask[None]] * batch_size)

       
        mask = torch.from_numpy(mask)

        target_shape = (batch_size, num_frames, 4, h //
                        scale_factor, w // scale_factor)

        if mask.shape != target_shape:
            raise ValueError(f"Make shape {mask.shape} != {target_shape}")

        return mask

    else:
        valid_mask_channel_sizes = [1, 3]
        # if mask channel is fourth tensor dimension, permute dimensions to pytorch standard (B, C, H, W)
        if mask.shape[3] in valid_mask_channel_sizes:
            mask = mask.permute(0, 3, 1, 2)
        elif mask.shape[1] not in valid_mask_channel_sizes:
            raise ValueError(
                f"Mask channel dimension of size in {valid_mask_channel_sizes} should be second or fourth dimension,"
                f" but received mask of shape {tuple(mask.shape)}"
            )
       
        mask = mask.mean(dim=1, keepdim=True)
        h, w = mask.shape[-2:]
        h, w = (x - x % 8 for x in (h, w))  # resize to integer multiple of 8
        mask = torch.nn.functional.interpolate(
            mask, (h // scale_factor, w // scale_factor))
        return mask


def _append_dims(x, target_dims):
    """Appends dimensions to the end of a tensor until it has target_dims dimensions."""
    dims_to_append = target_dims - x.ndim
    if dims_to_append < 0:
        raise ValueError(
            f"input has {x.ndim} dims but target_dims is {target_dims}, which is less")
    return x[(...,) + (None,) * dims_to_append]


def tensor2vid(video: torch.Tensor, processor, output_type="np"):
    # Based on:
    # https://github.com/modelscope/modelscope/blob/1509fdb973e5871f37148a4b5e5964cafd43e64d/modelscope/pipelines/multi_modal/text_to_video_synthesis_pipeline.py#L78

    batch_size, channels, num_frames, height, width = video.shape
    outputs = []
    for batch_idx in range(batch_size):
        batch_vid = video[batch_idx].permute(1, 0, 2, 3)
        batch_output = processor.postprocess(batch_vid, output_type)

        outputs.append(batch_output)
    

    return outputs

 
import torchvision.transforms.functional as TF

def _resize_with_antialiasing(image, target_size):
    """
    Resize the image to a target size with antialiasing.
    
    Parameters:
    image (torch.Tensor): The image tensor to resize.
    target_size (tuple): The target size as a tuple (width, height).
    
    Returns:
    torch.Tensor: The resized image tensor.
    """
    # Convert to PIL image if it's a tensor
    if isinstance(image, torch.Tensor):
        image = TF.to_pil_image(image[0])

    # Resize with antialiasing
    resized_image = image.resize(target_size, resample=PIL.Image.Resampling.LANCZOS)

    # Convert back to tensor
    resized_image = TF.to_tensor(resized_image)

    return resized_image

@dataclass
class MotionComDiffusionPipelineOutput(BaseOutput):
    r"""
    Output class for zero-shot text-to-video pipeline.

    Args:
        frames (`[List[PIL.Image.Image]`, `np.ndarray`]):
            List of denoised PIL images of length `batch_size` or NumPy array of shape `(batch_size, height, width,
            num_channels)`.
    """

    frames: Union[List[PIL.Image.Image], np.ndarray]


class MotionComDiffusionPipeline(DiffusionPipeline):
    r"""
    Pipeline to generate video from an input image using Stable Video Diffusion.

    This model inherits from [`DiffusionPipeline`]. Check the superclass documentation for the generic methods
    implemented for all pipelines (downloading, saving, running on a particular device, etc.).

    Args:
        vae ([`AutoencoderKL`]):
            Variational Auto-Encoder (VAE) model to encode and decode images to and from latent representations.
        image_encoder ([`~transformers.CLIPVisionModelWithProjection`]):
            Frozen CLIP image-encoder ([laion/CLIP-ViT-H-14-laion2B-s32B-b79K](https://huggingface.co/laion/CLIP-ViT-H-14-laion2B-s32B-b79K)).
        unet ([`UNetSpatioTemporalConditionModel`]):
            A `UNetSpatioTemporalConditionModel` to denoise the encoded image latents.
        scheduler ([`EulerDiscreteScheduler`]):
            A scheduler to be used in combination with `unet` to denoise the encoded image latents.
        feature_extractor ([`~transformers.CLIPImageProcessor`]):
            A `CLIPImageProcessor` to extract features from generated images.
    """

    model_cpu_offload_seq = "image_encoder->unet->vae"

    def __init__(
        self,
        vae: AutoencoderKLTemporalDecoder,
        image_encoder: CLIPVisionModelWithProjection,
        unet: UNetSpatioTemporalConditionModel,
        scheduler: EulerDiscreteScheduler,
        feature_extractor: CLIPImageProcessor,
    ):
        super().__init__()

        self.register_modules(
            vae=vae,
            image_encoder=image_encoder,
            unet=unet,
            scheduler=scheduler,
            feature_extractor=feature_extractor,
        )
        self.vae_scale_factor = 2 ** (
            len(self.vae.config.block_out_channels) - 1)
        self.image_processor = VaeImageProcessor(
            vae_scale_factor=self.vae_scale_factor)

    def _encode_image(self, image, device, num_videos_per_prompt, do_classifier_free_guidance):
        dtype = next(self.image_encoder.parameters()).dtype

        if not isinstance(image, torch.Tensor):
            image = self.image_processor.pil_to_numpy(image)
            image = self.image_processor.numpy_to_pt(image)

            # We normalize the image before resizing to match with the original implementation.
            # Then we unnormalize it after resizing.
            image = image * 2.0 - 1.0
            image = _resize_with_antialiasing(image, (224, 224))
            
            # image = image.resize((224, 224),ANTIALIAS)
            image = (image + 1.0) / 2.0

            # Normalize the image with for CLIP input
            image = self.feature_extractor(
                images=image,
                do_normalize=True,
                do_center_crop=False,
                do_resize=False,
                do_rescale=False,
                return_tensors="pt",
            ).pixel_values

        image = image.to(device=device, dtype=dtype)
        image_embeddings = self.image_encoder(image).image_embeds
        image_embeddings = image_embeddings.unsqueeze(1)

   
        bs_embed, seq_len, _ = image_embeddings.shape
        image_embeddings = image_embeddings.repeat(1, num_videos_per_prompt, 1)
        image_embeddings = image_embeddings.view(
            bs_embed * num_videos_per_prompt, seq_len, -1)

        if do_classifier_free_guidance:
            negative_image_embeddings = torch.zeros_like(image_embeddings)

            # For classifier free guidance, we need to do two forward passes.
            # Here we concatenate the unconditional and text embeddings into a single batch
            # to avoid doing two forward passes
            image_embeddings = torch.cat(
                [negative_image_embeddings, image_embeddings])

        return image_embeddings

    def _encode_vae_image(
        self,
        image: torch.Tensor,
        device,
        num_videos_per_prompt,
        do_classifier_free_guidance,
    ):
        image = image.to(device=device)
        image_latents = self.vae.encode(image).latent_dist.mode()

        if do_classifier_free_guidance:
            negative_image_latents = torch.zeros_like(image_latents)

            # For classifier free guidance, we need to do two forward passes.
            # Here we concatenate the unconditional and text embeddings into a single batch
            # to avoid doing two forward passes
            image_latents = torch.cat([negative_image_latents, image_latents])

        # duplicate image_latents for each generation per prompt, using mps friendly method
        image_latents = image_latents.repeat(num_videos_per_prompt, 1, 1, 1)

        return image_latents

    def _get_add_time_ids(
        self,
        fps,
        motion_bucket_id,
        noise_aug_strength,
        dtype,
        batch_size,
        num_videos_per_prompt,
        do_classifier_free_guidance,
    ):
        add_time_ids = [fps, motion_bucket_id, noise_aug_strength]

        passed_add_embed_dim = self.unet.config.addition_time_embed_dim * \
            len(add_time_ids)
        expected_add_embed_dim = self.unet.add_embedding.linear_1.in_features

        if expected_add_embed_dim != passed_add_embed_dim:
            raise ValueError(
                f"Model expects an added time embedding vector of length {expected_add_embed_dim}, but a vector of {passed_add_embed_dim} was created. The model has an incorrect config. Please check `unet.config.time_embedding_type` and `text_encoder_2.config.projection_dim`."
            )

        add_time_ids = torch.tensor([add_time_ids], dtype=dtype)
        add_time_ids = add_time_ids.repeat(
            batch_size * num_videos_per_prompt, 1)

        if do_classifier_free_guidance:
            add_time_ids = torch.cat([add_time_ids, add_time_ids])

        return add_time_ids

    def decode_latents(self, latents, num_frames, decode_chunk_size=14):
        # [batch, frames, channels, height, width] -> [batch*frames, channels, height, width]
        latents = latents.flatten(0, 1)

        latents = 1 / self.vae.config.scaling_factor * latents

        # decode decode_chunk_size frames at a time to avoid OOM
        frames = []
        for i in range(0, latents.shape[0], decode_chunk_size):
            num_frames_in = latents[i: i + decode_chunk_size].shape[0]
            frame = self.vae.decode(
                latents[i: i + decode_chunk_size], num_frames_in).sample
            frames.append(frame)
        frames = torch.cat(frames, dim=0)

        # [batch*frames, channels, height, width] -> [batch, channels, frames, height, width]
        frames = frames.reshape(-1, num_frames, *
                                frames.shape[1:]).permute(0, 2, 1, 3, 4)

        # we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
        frames = frames.float()
        return frames

    def check_inputs(self, image, height, width):
        if (
            not isinstance(image, torch.Tensor)
            and not isinstance(image, PIL.Image.Image)
            and not isinstance(image, list)
        ):
            raise ValueError(
                "`image` has to be of type `torch.FloatTensor` or `PIL.Image.Image` or `List[PIL.Image.Image]` but is"
                f" {type(image)}"
            )

        if height % 8 != 0 or width % 8 != 0:
            raise ValueError(
                f"`height` and `width` have to be divisible by 8 but are {height} and {width}.")

    def _prepare_latents_with_init_image(
        self,
        image,
        timestep,
        batch_size,
        num_frames,
        num_channels_latents,
        height,
        width,
        dtype,
        device,
        generator,
        latents=None,
    ):
        assert len(image.shape) == 4

        image = image.to(device=device, dtype=dtype)

        init_latent_dist = self.vae.encode(image).latent_dist
        init_latents = init_latent_dist.sample(generator=generator)
        init_latents = self.vae.config.scaling_factor * init_latents

        assert len(init_latents.shape) == 4

        init_latents = init_latents.unsqueeze(0)
        init_latents = torch.cat([init_latents] * num_frames, dim=1)
        init_latents = torch.cat([init_latents] * batch_size, dim=0)
        init_latents_orig = init_latents

        shape = (
            batch_size,
            num_frames,
            num_channels_latents // 2,
            height // self.vae_scale_factor,
            width // self.vae_scale_factor,
        )

        if init_latents.shape != shape:
            raise ValueError(
                f"Init latent shape {init_latents.shape} != {shape}"
            )

        # add noise to latents using the timesteps
        noise = randn_tensor(init_latents.shape,
                             generator=generator, device=device, dtype=dtype)
        latents = self.scheduler.add_noise(init_latents, noise, timestep)

        return latents, init_latents_orig, noise
    
    
    def prepare_latents(
        self,
        batch_size,
        num_frames,
        num_channels_latents,
        height,
        width,
        dtype,
        device,
        generator,
        latents=None,
        
    ):
        shape = (
            batch_size,
            num_frames,
            num_channels_latents // 2,
            height // self.vae_scale_factor,
            width // self.vae_scale_factor,
        )
        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."
            )
     
        if latents is None:
            latents = randn_tensor(
                shape, generator=generator, device=device, dtype=dtype)
           
        else:
            latents = latents.to(device)

        # scale the initial noise by the standard deviation required by the scheduler
        latents = latents * self.scheduler.init_noise_sigma
        return latents


   

    def generate_smoothed_noise(self,raw_noise, num_frames, window_size=2,dtype=None):
       
        # Apply a moving average filter across the frames
        smoothed_noise = torch.zeros_like(raw_noise)
        for frame_idx in range(num_frames):
            start_idx = max(frame_idx - window_size // 2, 0)
            end_idx = min(frame_idx + window_size // 2 + 1, num_frames)
            smoothed_noise[:, frame_idx] = raw_noise[:, start_idx:end_idx].mean(dim=1)
        
        return smoothed_noise
    
    

      
    @torch.no_grad()
  
    def __call__(
        self,
        image: Union[PIL.Image.Image, List[PIL.Image.Image], torch.FloatTensor],
        height: int = 576,
        width: int = 1024,
        num_frames: Optional[int] = None,
        num_inference_steps: int = 25,
        min_guidance_scale: float = 1.0,
        max_guidance_scale: float = 3.0,
        fps: int = 7,
        motion_bucket_id: int = 127,
        noise_aug_strength: int = 0.02,
        decode_chunk_size: Optional[int] = None,
        num_videos_per_prompt: Optional[int] = 1,
        generator: Optional[Union[torch.Generator,
                                  List[torch.Generator]]] = None,
        latents: Optional[torch.FloatTensor] = None,
        output_type: Optional[str] = "pil",
        return_dict: bool = True,
        overlay_init_image=None,
        overlay_mask_image=None,
        overlay_start=0.0,
        overlay_end=0.9,
        
    ):
        r"""
        The call function to the pipeline for generation.

        Args:
            image (`PIL.Image.Image` or `List[PIL.Image.Image]` or `torch.FloatTensor`):
                Image or images to guide image generation. If you provide a tensor, it needs to be compatible with
                [`CLIPImageProcessor`](https://huggingface.co/lambdalabs/sd-image-variations-diffusers/blob/main/feature_extractor/preprocessor_config.json).
            height (`int`, *optional*, defaults to `self.unet.config.sample_size * self.vae_scale_factor`):
                The height in pixels of the generated image.
            width (`int`, *optional*, defaults to `self.unet.config.sample_size * self.vae_scale_factor`):
                The width in pixels of the generated image.
            num_frames (`int`, *optional*):
                The number of video frames to generate. Defaults to 14 for `stable-video-diffusion-img2vid` and to 25 for `stable-video-diffusion-img2vid-xt`
            num_inference_steps (`int`, *optional*, defaults to 25):
                The number of denoising steps. More denoising steps usually lead to a higher quality image at the
                expense of slower inference. This parameter is modulated by `strength`.
            min_guidance_scale (`float`, *optional*, defaults to 1.0):
                The minimum guidance scale. Used for the classifier free guidance with first frame.
            max_guidance_scale (`float`, *optional*, defaults to 3.0):
                The maximum guidance scale. Used for the classifier free guidance with last frame.
            fps (`int`, *optional*, defaults to 7):
                Frames per second. The rate at which the generated images shall be exported to a video after generation.
                Note that Stable Diffusion Video's UNet was micro-conditioned on fps-1 during training.
            motion_bucket_id (`int`, *optional*, defaults to 127):
                The motion bucket ID. Used as conditioning for the generation. The higher the number the more motion will be in the video.
            noise_aug_strength (`int`, *optional*, defaults to 0.02):
                The amount of noise added to the init image, the higher it is the less the video will look like the init image. Increase it for more motion.
            decode_chunk_size (`int`, *optional*):
                The number of frames to decode at a time. The higher the chunk size, the higher the temporal consistency
                between frames, but also the higher the memory consumption. By default, the decoder will decode all frames at once
                for maximal quality. Reduce `decode_chunk_size` to reduce memory usage.
            num_videos_per_prompt (`int`, *optional*, defaults to 1):
                The number of images to generate per prompt.
            generator (`torch.Generator` or `List[torch.Generator]`, *optional*):
                A [`torch.Generator`](https://pytorch.org/docs/stable/generated/torch.Generator.html) to make
                generation deterministic.
            latents (`torch.FloatTensor`, *optional*):
                Pre-generated noisy latents sampled from a Gaussian distribution, to be used as inputs for image
                generation. Can be used to tweak the same generation with different prompts. If not provided, a latents
                tensor is generated by sampling using the supplied random `generator`.
            output_type (`str`, *optional*, defaults to `"pil"`):
                The output format of the generated image. Choose between `PIL.Image` or `np.array`.
            return_dict (`bool`, *optional*, defaults to `True`):
                Whether or not to return a [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] instead of a
                plain tuple.

        Returns:
            [`~pipelines.stable_diffusion.StableVideoDiffusionPipelineOutput`] or `tuple`:
                If `return_dict` is `True`, [`~pipelines.stable_diffusion.StableVideoDiffusionPipelineOutput`] is returned,
                otherwise a `tuple` is returned where the first element is a list of list with the generated frames.

        Examples:

        ```py
        from diffusers import StableVideoDiffusionInpaintingPipeline
        from diffusers.utils import load_image, export_to_video

        pipe = StableVideoDiffusionInpaintingPipeline.from_pretrained("stabilityai/stable-video-diffusion-img2vid-xt", torch_dtype=torch.float16, variant="fp16")
        pipe.to("cuda")

        image = load_image("https://lh3.googleusercontent.com/y-iFOHfLTwkuQSUegpwDdgKmOjRSTvPxat63dQLB25xkTs4lhIbRUFeNBWZzYf370g=s1200")
        image = image.resize((1024, 576))

        frames = pipe(image, num_frames=25, decode_chunk_size=8).frames[0]
        export_to_video(frames, "generated.mp4", fps=7)
        ```
        """
        # 0. Default height and width to unet
        height = height or self.unet.config.sample_size * self.vae_scale_factor
        width = width or self.unet.config.sample_size * self.vae_scale_factor

        from diffusers.utils import load_image
        
         
        use_overlay = overlay_init_image is not None and overlay_mask_image is not None

        num_frames = num_frames if num_frames is not None else self.unet.config.num_frames
        decode_chunk_size = decode_chunk_size if decode_chunk_size is not None else num_frames

        # 1. Check inputs. Raise error if not correct
        self.check_inputs(image, height, width)

        # 2. Define call parameters
        if isinstance(image, PIL.Image.Image):
            batch_size = 1
        elif isinstance(image, list):
            batch_size = len(image)
        else:
            batch_size = image.shape[0]
        device = self._execution_device
        # here `guidance_scale` is defined analog to the guidance weight `w` of equation (2)
        # of the Imagen paper: https://arxiv.org/pdf/2205.11487.pdf . `guidance_scale = 1`
        # corresponds to doing no classifier free guidance.
        do_classifier_free_guidance = max_guidance_scale > 1.0

         # 4. Prepare timesteps
        self.scheduler.set_timesteps(num_inference_steps, device=device)
        timesteps = self.scheduler.timesteps
       
        latent_timestep = timesteps[:1].repeat(
            batch_size * num_videos_per_prompt
        )

        # 3. Encode input image
        image_embeddings = self._encode_image(
            image, device, num_videos_per_prompt, do_classifier_free_guidance)


        # NOTE: Stable Diffusion Video was conditioned on fps - 1, which
        # is why it is reduced here.
        # See: https://github.com/Stability-AI/generative-models/blob/ed0997173f98eaf8f4edf7ba5fe8f15c6b877fd3/scripts/sampling/simple_video_sample.py#L188
        fps = fps - 1
 
        # 4. Encode input image using VAE
        image = self.image_processor.preprocess(
            image, height=height, width=width)
        image = image + noise_aug_strength * torch.randn_like(image)

        needs_upcasting = self.vae.dtype == torch.float16 and self.vae.config.force_upcast
        if needs_upcasting:
            self.vae.to(dtype=torch.float32)

        image_latents = self._encode_vae_image(
            image, device, num_videos_per_prompt, do_classifier_free_guidance)
        image_latents = image_latents.to(image_embeddings.dtype)

        # cast back to fp16 if needed
        if needs_upcasting:
            self.vae.to(dtype=torch.float16)

        # Repeat the image latents for each frame so we can concatenate them with the noise
        # image_latents [batch, channels, height, width] ->[batch, num_frames, channels, height, width]
        image_latents = image_latents.unsqueeze(
            1).repeat(1, num_frames, 1, 1, 1)
       
        
        # 5. Get Added Time IDs
        added_time_ids = self._get_add_time_ids(
            fps,
            motion_bucket_id,
            noise_aug_strength,
            image_embeddings.dtype,
            batch_size,
            num_videos_per_prompt,
            do_classifier_free_guidance,
        )
        added_time_ids = added_time_ids.to(device)

       

        # 5. Prepare latent variables
        num_channels_latents = self.unet.config.in_channels
        latents = self.prepare_latents(
            batch_size * num_videos_per_prompt,
            num_frames,
            num_channels_latents,
            height,
            width,
            image_embeddings.dtype,
            device,
            generator,
            latents,
            
        )
        
        init_latents_orig = None
        noise = None
        overlay_mask = None
        if use_overlay:
            overlay_init_image = preprocess_image(
                image=overlay_init_image,
                batch_size=batch_size,
            ) if not isinstance(
                overlay_init_image, torch.FloatTensor
            ) else overlay_init_image

           
             
            overlay_mask_image = preprocess_mask(
                overlay_mask_image,
                batch_size=batch_size,
                num_frames=num_frames,
                scale_factor=self.vae_scale_factor,
            )

            overlay_mask = overlay_mask_image.to(
                device=device, dtype=latents.dtype)
            overlay_mask = torch.cat([overlay_mask] * num_videos_per_prompt)

            _, init_latents_orig, noise = self._prepare_latents_with_init_image(
                image=overlay_init_image,
                timestep=latent_timestep,
                num_frames=num_frames,
                num_channels_latents=num_channels_latents,
                batch_size=batch_size * num_videos_per_prompt,
                dtype=image_embeddings.dtype,
                device=device,
                width=width,
                height=height,
                generator=generator,
            )
            
            
            if init_latents_orig.shape != latents.shape:
                raise ValueError(
                    f"Init latents shape {init_latents_orig.shape} != {latents.shape}"
                )
            
     
        
        # 7. Prepare guidance scale
        guidance_scale = torch.linspace(
            min_guidance_scale, max_guidance_scale, num_frames).unsqueeze(0)
        guidance_scale = guidance_scale.to(device, latents.dtype)
        guidance_scale = guidance_scale.repeat(
            batch_size * num_videos_per_prompt, 1)
        guidance_scale = _append_dims(guidance_scale, latents.ndim)

        overlay_start_index = int(overlay_start * num_inference_steps)
        overlay_end_index = int(overlay_end * num_inference_steps)
        
        # 8. Denoising loop 
      
        num_warmup_steps = len(timesteps) - \
            num_inference_steps * self.scheduler.order
       
        with self.progress_bar(total=num_inference_steps) as progress_bar:
            for i, t in enumerate(timesteps):
              
                latent_model_input = torch.cat(
                    [latents] * 2) if do_classifier_free_guidance else latents
                    
                latent_model_input = self.scheduler.scale_model_input(
                    latent_model_input, t)

                # Concatenate image_latents over channels dimention
                latent_model_input = torch.cat(
                    [latent_model_input, image_latents], dim=2)

                # predict the noise residual
                noise_pred = self.unet(
                    latent_model_input,
                    t,
                    encoder_hidden_states=image_embeddings,
                    added_time_ids=added_time_ids,
                    return_dict=False
                )[0]

                # perform guidance
                if do_classifier_free_guidance:
                    noise_pred_uncond, noise_pred_cond = noise_pred.chunk(2)
                    noise_pred = noise_pred_uncond + guidance_scale * \
                        (noise_pred_cond - noise_pred_uncond)

                # compute the previous noisy sample x_t -> x_t-1
                latents = self.scheduler.step(
                    noise_pred, t, latents).prev_sample

              
                if use_overlay and i >= overlay_start_index and i < overlay_end_index:
                 
                    noise_timestep = timesteps[i+1]
                    init_latents_proper = self.scheduler.add_noise(
                        init_latents_orig, noise, torch.tensor([noise_timestep])
                    )
                  
                    latents = (init_latents_proper* (1-overlay_mask)) + latents * (overlay_mask) ###fg (white) is inpainted with new xt.
                    
            
                if i == len(timesteps) - 1 or ((i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0):
                    progress_bar.update()

        if not output_type == "latent":
            # cast back to fp16 if needed
            if needs_upcasting:
                self.vae.to(dtype=torch.float16)
            frames = self.decode_latents(
                latents, num_frames, decode_chunk_size)
            
            frames = tensor2vid(frames, self.image_processor,
                                output_type=output_type)
        else:
            frames = latents

        self.maybe_free_model_hooks()

        if not return_dict:
            return frames

        return MotionComDiffusionPipelineOutput(frames=frames)