# Copyright 2023 Pix2Pix Zero Authors and The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

import inspect
from dataclasses import dataclass
from typing import Any, Callable, Dict, List, Optional, Union

import numpy as np
import PIL
import torch
import torch.nn.functional as F
from transformers import (
    BlipForConditionalGeneration,
    BlipProcessor,
    CLIPImageProcessor,
    CLIPTextModel,
    CLIPTokenizer,
)

from ...image_processor import PipelineImageInput, VaeImageProcessor
from ...loaders import LoraLoaderMixin, TextualInversionLoaderMixin
from ...models import AutoencoderKL, UNet2DConditionModel
from ...models.attention_processor import Attention
from ...models.lora import adjust_lora_scale_text_encoder
from ...schedulers import DDIMScheduler, DDPMScheduler, EulerAncestralDiscreteScheduler, LMSDiscreteScheduler
from ...schedulers.scheduling_ddim_inverse import DDIMInverseScheduler
from ...utils import (
    PIL_INTERPOLATION,
    BaseOutput,
    deprecate,
    logging,
    replace_example_docstring,
)
from ...utils.torch_utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline
from . import StableDiffusionPipelineOutput
from .safety_checker import StableDiffusionSafetyChecker


logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


@dataclass
class Pix2PixInversionPipelineOutput(BaseOutput, TextualInversionLoaderMixin):
    """
    Output class for Stable Diffusion pipelines.

    Args:
        latents (`torch.FloatTensor`)
            inverted latents tensor
        images (`List[PIL.Image.Image]` or `np.ndarray`)
            List of denoised PIL images of length `batch_size` or numpy array of shape `(batch_size, height, width,
            num_channels)`. PIL images or numpy array present the denoised images of the diffusion pipeline.
    """

    latents: torch.FloatTensor
    images: Union[List[PIL.Image.Image], np.ndarray]


EXAMPLE_DOC_STRING = """
    Examples:
        ```py
        >>> import requests
        >>> import torch

        >>> from diffusers import DDIMScheduler, StableDiffusionPix2PixZeroPipeline


        >>> def download(embedding_url, local_filepath):
        ...     r = requests.get(embedding_url)
        ...     with open(local_filepath, "wb") as f:
        ...         f.write(r.content)


        >>> model_ckpt = "CompVis/stable-diffusion-v1-4"
        >>> pipeline = StableDiffusionPix2PixZeroPipeline.from_pretrained(model_ckpt, torch_dtype=torch.float16)
        >>> pipeline.scheduler = DDIMScheduler.from_config(pipeline.scheduler.config)
        >>> pipeline.to("cuda")

        >>> prompt = "a high resolution painting of a cat in the style of van gough"
        >>> source_emb_url = "https://hf.co/datasets/sayakpaul/sample-datasets/resolve/main/cat.pt"
        >>> target_emb_url = "https://hf.co/datasets/sayakpaul/sample-datasets/resolve/main/dog.pt"

        >>> for url in [source_emb_url, target_emb_url]:
        ...     download(url, url.split("/")[-1])

        >>> src_embeds = torch.load(source_emb_url.split("/")[-1])
        >>> target_embeds = torch.load(target_emb_url.split("/")[-1])
        >>> images = pipeline(
        ...     prompt,
        ...     source_embeds=src_embeds,
        ...     target_embeds=target_embeds,
        ...     num_inference_steps=50,
        ...     cross_attention_guidance_amount=0.15,
        ... ).images

        >>> images[0].save("edited_image_dog.png")
        ```
"""

EXAMPLE_INVERT_DOC_STRING = """
    Examples:
        ```py
        >>> import torch
        >>> from transformers import BlipForConditionalGeneration, BlipProcessor
        >>> from diffusers import DDIMScheduler, DDIMInverseScheduler, StableDiffusionPix2PixZeroPipeline

        >>> import requests
        >>> from PIL import Image

        >>> captioner_id = "Salesforce/blip-image-captioning-base"
        >>> processor = BlipProcessor.from_pretrained(captioner_id)
        >>> model = BlipForConditionalGeneration.from_pretrained(
        ...     captioner_id, torch_dtype=torch.float16, low_cpu_mem_usage=True
        ... )

        >>> sd_model_ckpt = "CompVis/stable-diffusion-v1-4"
        >>> pipeline = StableDiffusionPix2PixZeroPipeline.from_pretrained(
        ...     sd_model_ckpt,
        ...     caption_generator=model,
        ...     caption_processor=processor,
        ...     torch_dtype=torch.float16,
        ...     safety_checker=None,
        ... )

        >>> pipeline.scheduler = DDIMScheduler.from_config(pipeline.scheduler.config)
        >>> pipeline.inverse_scheduler = DDIMInverseScheduler.from_config(pipeline.scheduler.config)
        >>> pipeline.enable_model_cpu_offload()

        >>> img_url = "https://github.com/pix2pixzero/pix2pix-zero/raw/main/assets/test_images/cats/cat_6.png"

        >>> raw_image = Image.open(requests.get(img_url, stream=True).raw).convert("RGB").resize((512, 512))
        >>> # generate caption
        >>> caption = pipeline.generate_caption(raw_image)

        >>> # "a photography of a cat with flowers and dai dai daie - daie - daie kasaii"
        >>> inv_latents = pipeline.invert(caption, image=raw_image).latents
        >>> # we need to generate source and target embeds

        >>> source_prompts = ["a cat sitting on the street", "a cat playing in the field", "a face of a cat"]

        >>> target_prompts = ["a dog sitting on the street", "a dog playing in the field", "a face of a dog"]

        >>> source_embeds = pipeline.get_embeds(source_prompts)
        >>> target_embeds = pipeline.get_embeds(target_prompts)
        >>> # the latents can then be used to edit a real image
        >>> # when using Stable Diffusion 2 or other models that use v-prediction
        >>> # set `cross_attention_guidance_amount` to 0.01 or less to avoid input latent gradient explosion

        >>> image = pipeline(
        ...     caption,
        ...     source_embeds=source_embeds,
        ...     target_embeds=target_embeds,
        ...     num_inference_steps=50,
        ...     cross_attention_guidance_amount=0.15,
        ...     generator=generator,
        ...     latents=inv_latents,
        ...     negative_prompt=caption,
        ... ).images[0]
        >>> image.save("edited_image.png")
        ```
"""


# Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion_img2img.preprocess
def preprocess(image):
    deprecation_message = "The preprocess method is deprecated and will be removed in diffusers 1.0.0. Please use VaeImageProcessor.preprocess(...) instead"
    deprecate("preprocess", "1.0.0", deprecation_message, standard_warn=False)
    if isinstance(image, torch.Tensor):
        return image
    elif isinstance(image, PIL.Image.Image):
        image = [image]

    if isinstance(image[0], PIL.Image.Image):
        w, h = image[0].size
        w, h = (x - x % 8 for x in (w, h))  # resize to integer multiple of 8

        image = [np.array(i.resize((w, h), resample=PIL_INTERPOLATION["lanczos"]))[None, :] for i in image]
        image = np.concatenate(image, axis=0)
        image = np.array(image).astype(np.float32) / 255.0
        image = image.transpose(0, 3, 1, 2)
        image = 2.0 * image - 1.0
        image = torch.from_numpy(image)
    elif isinstance(image[0], torch.Tensor):
        image = torch.cat(image, dim=0)
    return image


def prepare_unet(unet: UNet2DConditionModel):
    """Modifies the UNet (`unet`) to perform Pix2Pix Zero optimizations."""
    pix2pix_zero_attn_procs = {}
    for name in unet.attn_processors.keys():
        module_name = name.replace(".processor", "")
        module = unet.get_submodule(module_name)
        if "attn2" in name:
            pix2pix_zero_attn_procs[name] = Pix2PixZeroAttnProcessor(is_pix2pix_zero=True)
            module.requires_grad_(True)
        else:
            pix2pix_zero_attn_procs[name] = Pix2PixZeroAttnProcessor(is_pix2pix_zero=False)
            module.requires_grad_(False)

    unet.set_attn_processor(pix2pix_zero_attn_procs)
    return unet


class Pix2PixZeroL2Loss:
    def __init__(self):
        self.loss = 0.0

    def compute_loss(self, predictions, targets):
        self.loss += ((predictions - targets) ** 2).sum((1, 2)).mean(0)


class Pix2PixZeroAttnProcessor:
    """An attention processor class to store the attention weights.
    In Pix2Pix Zero, it happens during computations in the cross-attention blocks."""

    def __init__(self, is_pix2pix_zero=False):
        self.is_pix2pix_zero = is_pix2pix_zero
        if self.is_pix2pix_zero:
            self.reference_cross_attn_map = {}

    def __call__(
        self,
        attn: Attention,
        hidden_states,
        encoder_hidden_states=None,
        attention_mask=None,
        timestep=None,
        loss=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)

        attention_probs = attn.get_attention_scores(query, key, attention_mask)
        if self.is_pix2pix_zero and timestep is not None:
            # new bookkeeping to save the attention weights.
            if loss is None:
                self.reference_cross_attn_map[timestep.item()] = attention_probs.detach().cpu()
            # compute loss
            elif loss is not None:
                prev_attn_probs = self.reference_cross_attn_map.pop(timestep.item())
                loss.compute_loss(attention_probs, prev_attn_probs.to(attention_probs.device))

        hidden_states = torch.bmm(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


class StableDiffusionPix2PixZeroPipeline(DiffusionPipeline):
    r"""
    Pipeline for pixel-levl image editing using Pix2Pix Zero. Based on Stable Diffusion.

    This model inherits from [`DiffusionPipeline`]. Check the superclass documentation for the generic methods the
    library implements for all the pipelines (such as downloading or 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.
        text_encoder ([`CLIPTextModel`]):
            Frozen text-encoder. Stable Diffusion uses the text portion of
            [CLIP](https://huggingface.co/docs/transformers/model_doc/clip#transformers.CLIPTextModel), specifically
            the [clip-vit-large-patch14](https://huggingface.co/openai/clip-vit-large-patch14) variant.
        tokenizer (`CLIPTokenizer`):
            Tokenizer of class
            [CLIPTokenizer](https://huggingface.co/docs/transformers/v4.21.0/en/model_doc/clip#transformers.CLIPTokenizer).
        unet ([`UNet2DConditionModel`]): Conditional U-Net architecture to denoise the encoded image latents.
        scheduler ([`SchedulerMixin`]):
            A scheduler to be used in combination with `unet` to denoise the encoded image latents. Can be one of
            [`DDIMScheduler`], [`LMSDiscreteScheduler`], [`EulerAncestralDiscreteScheduler`], or [`DDPMScheduler`].
        safety_checker ([`StableDiffusionSafetyChecker`]):
            Classification module that estimates whether generated images could be considered offensive or harmful.
            Please, refer to the [model card](https://huggingface.co/runwayml/stable-diffusion-v1-5) for details.
        feature_extractor ([`CLIPImageProcessor`]):
            Model that extracts features from generated images to be used as inputs for the `safety_checker`.
        requires_safety_checker (bool):
            Whether the pipeline requires a safety checker. We recommend setting it to True if you're using the
            pipeline publicly.
    """
    model_cpu_offload_seq = "text_encoder->unet->vae"
    _optional_components = [
        "safety_checker",
        "feature_extractor",
        "caption_generator",
        "caption_processor",
        "inverse_scheduler",
    ]
    _exclude_from_cpu_offload = ["safety_checker"]

    def __init__(
        self,
        vae: AutoencoderKL,
        text_encoder: CLIPTextModel,
        tokenizer: CLIPTokenizer,
        unet: UNet2DConditionModel,
        scheduler: Union[DDPMScheduler, DDIMScheduler, EulerAncestralDiscreteScheduler, LMSDiscreteScheduler],
        feature_extractor: CLIPImageProcessor,
        safety_checker: StableDiffusionSafetyChecker,
        inverse_scheduler: DDIMInverseScheduler,
        caption_generator: BlipForConditionalGeneration,
        caption_processor: BlipProcessor,
        requires_safety_checker: bool = True,
    ):
        super().__init__()

        if safety_checker is None and requires_safety_checker:
            logger.warning(
                f"You have disabled the safety checker for {self.__class__} by passing `safety_checker=None`. Ensure"
                " that you abide to the conditions of the Stable Diffusion license and do not expose unfiltered"
                " results in services or applications open to the public. Both the diffusers team and Hugging Face"
                " strongly recommend to keep the safety filter enabled in all public facing circumstances, disabling"
                " it only for use-cases that involve analyzing network behavior or auditing its results. For more"
                " information, please have a look at https://github.com/huggingface/diffusers/pull/254 ."
            )

        if safety_checker is not None and feature_extractor is None:
            raise ValueError(
                "Make sure to define a feature extractor when loading {self.__class__} if you want to use the safety"
                " checker. If you do not want to use the safety checker, you can pass `'safety_checker=None'` instead."
            )

        self.register_modules(
            vae=vae,
            text_encoder=text_encoder,
            tokenizer=tokenizer,
            unet=unet,
            scheduler=scheduler,
            safety_checker=safety_checker,
            feature_extractor=feature_extractor,
            caption_processor=caption_processor,
            caption_generator=caption_generator,
            inverse_scheduler=inverse_scheduler,
        )
        self.vae_scale_factor = 2 ** (len(self.vae.config.block_out_channels) - 1)
        self.image_processor = VaeImageProcessor(vae_scale_factor=self.vae_scale_factor)
        self.register_to_config(requires_safety_checker=requires_safety_checker)

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline._encode_prompt
    def _encode_prompt(
        self,
        prompt,
        device,
        num_images_per_prompt,
        do_classifier_free_guidance,
        negative_prompt=None,
        prompt_embeds: Optional[torch.FloatTensor] = None,
        negative_prompt_embeds: Optional[torch.FloatTensor] = None,
        lora_scale: Optional[float] = None,
    ):
        deprecation_message = "`_encode_prompt()` is deprecated and it will be removed in a future version. Use `encode_prompt()` instead. Also, be aware that the output format changed from a concatenated tensor to a tuple."
        deprecate("_encode_prompt()", "1.0.0", deprecation_message, standard_warn=False)

        prompt_embeds_tuple = self.encode_prompt(
            prompt=prompt,
            device=device,
            num_images_per_prompt=num_images_per_prompt,
            do_classifier_free_guidance=do_classifier_free_guidance,
            negative_prompt=negative_prompt,
            prompt_embeds=prompt_embeds,
            negative_prompt_embeds=negative_prompt_embeds,
            lora_scale=lora_scale,
        )

        # concatenate for backwards comp
        prompt_embeds = torch.cat([prompt_embeds_tuple[1], prompt_embeds_tuple[0]])

        return prompt_embeds

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.encode_prompt
    def encode_prompt(
        self,
        prompt,
        device,
        num_images_per_prompt,
        do_classifier_free_guidance,
        negative_prompt=None,
        prompt_embeds: Optional[torch.FloatTensor] = None,
        negative_prompt_embeds: Optional[torch.FloatTensor] = None,
        lora_scale: Optional[float] = None,
    ):
        r"""
        Encodes the prompt into text encoder hidden states.

        Args:
            prompt (`str` or `List[str]`, *optional*):
                prompt to be encoded
            device: (`torch.device`):
                torch device
            num_images_per_prompt (`int`):
                number of images that should be generated per prompt
            do_classifier_free_guidance (`bool`):
                whether to use classifier free guidance or not
            negative_prompt (`str` or `List[str]`, *optional*):
                The prompt or prompts not to guide the image generation. If not defined, one has to pass
                `negative_prompt_embeds` instead. Ignored when not using guidance (i.e., ignored if `guidance_scale` is
                less than `1`).
            prompt_embeds (`torch.FloatTensor`, *optional*):
                Pre-generated text embeddings. Can be used to easily tweak text inputs, *e.g.* prompt weighting. If not
                provided, text embeddings will be generated from `prompt` input argument.
            negative_prompt_embeds (`torch.FloatTensor`, *optional*):
                Pre-generated negative text embeddings. Can be used to easily tweak text inputs, *e.g.* prompt
                weighting. If not provided, negative_prompt_embeds will be generated from `negative_prompt` input
                argument.
            lora_scale (`float`, *optional*):
                A lora scale that will be applied to all LoRA layers of the text encoder if LoRA layers are loaded.
        """
        # set lora scale so that monkey patched LoRA
        # function of text encoder can correctly access it
        if lora_scale is not None and isinstance(self, LoraLoaderMixin):
            self._lora_scale = lora_scale

            # dynamically adjust the LoRA scale
            adjust_lora_scale_text_encoder(self.text_encoder, lora_scale)

        if prompt is not None and isinstance(prompt, str):
            batch_size = 1
        elif prompt is not None and isinstance(prompt, list):
            batch_size = len(prompt)
        else:
            batch_size = prompt_embeds.shape[0]

        if prompt_embeds is None:
            # textual inversion: procecss multi-vector tokens if necessary
            if isinstance(self, TextualInversionLoaderMixin):
                prompt = self.maybe_convert_prompt(prompt, self.tokenizer)

            text_inputs = self.tokenizer(
                prompt,
                padding="max_length",
                max_length=self.tokenizer.model_max_length,
                truncation=True,
                return_tensors="pt",
            )
            text_input_ids = text_inputs.input_ids
            untruncated_ids = self.tokenizer(prompt, padding="longest", return_tensors="pt").input_ids

            if untruncated_ids.shape[-1] >= text_input_ids.shape[-1] and not torch.equal(
                text_input_ids, untruncated_ids
            ):
                removed_text = self.tokenizer.batch_decode(
                    untruncated_ids[:, self.tokenizer.model_max_length - 1 : -1]
                )
                logger.warning(
                    "The following part of your input was truncated because CLIP can only handle sequences up to"
                    f" {self.tokenizer.model_max_length} tokens: {removed_text}"
                )

            if hasattr(self.text_encoder.config, "use_attention_mask") and self.text_encoder.config.use_attention_mask:
                attention_mask = text_inputs.attention_mask.to(device)
            else:
                attention_mask = None

            prompt_embeds = self.text_encoder(
                text_input_ids.to(device),
                attention_mask=attention_mask,
            )
            prompt_embeds = prompt_embeds[0]

        if self.text_encoder is not None:
            prompt_embeds_dtype = self.text_encoder.dtype
        elif self.unet is not None:
            prompt_embeds_dtype = self.unet.dtype
        else:
            prompt_embeds_dtype = prompt_embeds.dtype

        prompt_embeds = prompt_embeds.to(dtype=prompt_embeds_dtype, device=device)

        bs_embed, seq_len, _ = prompt_embeds.shape
        # duplicate text embeddings for each generation per prompt, using mps friendly method
        prompt_embeds = prompt_embeds.repeat(1, num_images_per_prompt, 1)
        prompt_embeds = prompt_embeds.view(bs_embed * num_images_per_prompt, seq_len, -1)

        # get unconditional embeddings for classifier free guidance
        if do_classifier_free_guidance and negative_prompt_embeds is None:
            uncond_tokens: List[str]
            if negative_prompt is None:
                uncond_tokens = [""] * batch_size
            elif prompt is not None and type(prompt) is not type(negative_prompt):
                raise TypeError(
                    f"`negative_prompt` should be the same type to `prompt`, but got {type(negative_prompt)} !="
                    f" {type(prompt)}."
                )
            elif isinstance(negative_prompt, str):
                uncond_tokens = [negative_prompt]
            elif batch_size != len(negative_prompt):
                raise ValueError(
                    f"`negative_prompt`: {negative_prompt} has batch size {len(negative_prompt)}, but `prompt`:"
                    f" {prompt} has batch size {batch_size}. Please make sure that passed `negative_prompt` matches"
                    " the batch size of `prompt`."
                )
            else:
                uncond_tokens = negative_prompt

            # textual inversion: procecss multi-vector tokens if necessary
            if isinstance(self, TextualInversionLoaderMixin):
                uncond_tokens = self.maybe_convert_prompt(uncond_tokens, self.tokenizer)

            max_length = prompt_embeds.shape[1]
            uncond_input = self.tokenizer(
                uncond_tokens,
                padding="max_length",
                max_length=max_length,
                truncation=True,
                return_tensors="pt",
            )

            if hasattr(self.text_encoder.config, "use_attention_mask") and self.text_encoder.config.use_attention_mask:
                attention_mask = uncond_input.attention_mask.to(device)
            else:
                attention_mask = None

            negative_prompt_embeds = self.text_encoder(
                uncond_input.input_ids.to(device),
                attention_mask=attention_mask,
            )
            negative_prompt_embeds = negative_prompt_embeds[0]

        if do_classifier_free_guidance:
            # duplicate unconditional embeddings for each generation per prompt, using mps friendly method
            seq_len = negative_prompt_embeds.shape[1]

            negative_prompt_embeds = negative_prompt_embeds.to(dtype=prompt_embeds_dtype, device=device)

            negative_prompt_embeds = negative_prompt_embeds.repeat(1, num_images_per_prompt, 1)
            negative_prompt_embeds = negative_prompt_embeds.view(batch_size * num_images_per_prompt, seq_len, -1)

        return prompt_embeds, negative_prompt_embeds

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.run_safety_checker
    def run_safety_checker(self, image, device, dtype):
        if self.safety_checker is None:
            has_nsfw_concept = None
        else:
            if torch.is_tensor(image):
                feature_extractor_input = self.image_processor.postprocess(image, output_type="pil")
            else:
                feature_extractor_input = self.image_processor.numpy_to_pil(image)
            safety_checker_input = self.feature_extractor(feature_extractor_input, return_tensors="pt").to(device)
            image, has_nsfw_concept = self.safety_checker(
                images=image, clip_input=safety_checker_input.pixel_values.to(dtype)
            )
        return image, has_nsfw_concept

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.decode_latents
    def decode_latents(self, latents):
        deprecation_message = "The decode_latents method is deprecated and will be removed in 1.0.0. Please use VaeImageProcessor.postprocess(...) instead"
        deprecate("decode_latents", "1.0.0", deprecation_message, standard_warn=False)

        latents = 1 / self.vae.config.scaling_factor * latents
        image = self.vae.decode(latents, return_dict=False)[0]
        image = (image / 2 + 0.5).clamp(0, 1)
        # we always cast to float32 as this does not cause significant overhead and is compatible with bfloat16
        image = image.cpu().permute(0, 2, 3, 1).float().numpy()
        return image

    # Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.prepare_extra_step_kwargs
    def prepare_extra_step_kwargs(self, generator, eta):
        # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
        # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
        # eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
        # and should be between [0, 1]

        accepts_eta = "eta" in set(inspect.signature(self.scheduler.step).parameters.keys())
        extra_step_kwargs = {}
        if accepts_eta:
            extra_step_kwargs["eta"] = eta

        # check if the scheduler accepts generator
        accepts_generator = "generator" in set(inspect.signature(self.scheduler.step).parameters.keys())
        if accepts_generator:
            extra_step_kwargs["generator"] = generator
        return extra_step_kwargs

    def check_inputs(
        self,
        prompt,
        source_embeds,
        target_embeds,
        callback_steps,
        prompt_embeds=None,
    ):
        if (callback_steps is None) or (
            callback_steps is not None and (not isinstance(callback_steps, int) or callback_steps <= 0)
        ):
            raise ValueError(
                f"`callback_steps` has to be a positive integer but is {callback_steps} of type"
                f" {type(callback_steps)}."
            )
        if source_embeds is None and target_embeds is None:
            raise ValueError("`source_embeds` and `target_embeds` cannot be undefined.")

        if prompt is not None and prompt_embeds is not None:
            raise ValueError(
                f"Cannot forward both `prompt`: {prompt} and `prompt_embeds`: {prompt_embeds}. Please make sure to"
                " only forward one of the two."
            )
        elif prompt is None and prompt_embeds is None:
            raise ValueError(
                "Provide either `prompt` or `prompt_embeds`. Cannot leave both `prompt` and `prompt_embeds` undefined."
            )
        elif prompt is not None and (not isinstance(prompt, str) and not isinstance(prompt, list)):
            raise ValueError(f"`prompt` has to be of type `str` or `list` but is {type(prompt)}")

    #  Copied from diffusers.pipelines.stable_diffusion.pipeline_stable_diffusion.StableDiffusionPipeline.prepare_latents
    def prepare_latents(self, batch_size, num_channels_latents, height, width, dtype, device, generator, latents=None):
        shape = (batch_size, num_channels_latents, 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

    @torch.no_grad()
    def generate_caption(self, images):
        """Generates caption for a given image."""
        text = "a photography of"

        prev_device = self.caption_generator.device

        device = self._execution_device
        inputs = self.caption_processor(images, text, return_tensors="pt").to(
            device=device, dtype=self.caption_generator.dtype
        )
        self.caption_generator.to(device)
        outputs = self.caption_generator.generate(**inputs, max_new_tokens=128)

        # offload caption generator
        self.caption_generator.to(prev_device)

        caption = self.caption_processor.batch_decode(outputs, skip_special_tokens=True)[0]
        return caption

    def construct_direction(self, embs_source: torch.Tensor, embs_target: torch.Tensor):
        """Constructs the edit direction to steer the image generation process semantically."""
        return (embs_target.mean(0) - embs_source.mean(0)).unsqueeze(0)

    @torch.no_grad()
    def get_embeds(self, prompt: List[str], batch_size: int = 16) -> torch.FloatTensor:
        num_prompts = len(prompt)
        embeds = []
        for i in range(0, num_prompts, batch_size):
            prompt_slice = prompt[i : i + batch_size]

            input_ids = self.tokenizer(
                prompt_slice,
                padding="max_length",
                max_length=self.tokenizer.model_max_length,
                truncation=True,
                return_tensors="pt",
            ).input_ids

            input_ids = input_ids.to(self.text_encoder.device)
            embeds.append(self.text_encoder(input_ids)[0])

        return torch.cat(embeds, dim=0).mean(0)[None]

    def prepare_image_latents(self, image, batch_size, dtype, device, generator=None):
        if not isinstance(image, (torch.Tensor, PIL.Image.Image, list)):
            raise ValueError(
                f"`image` has to be of type `torch.Tensor`, `PIL.Image.Image` or list but is {type(image)}"
            )

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

        if image.shape[1] == 4:
            latents = image

        else:
            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 isinstance(generator, list):
                latents = [
                    self.vae.encode(image[i : i + 1]).latent_dist.sample(generator[i]) for i in range(batch_size)
                ]
                latents = torch.cat(latents, dim=0)
            else:
                latents = self.vae.encode(image).latent_dist.sample(generator)

            latents = self.vae.config.scaling_factor * latents

        if batch_size != latents.shape[0]:
            if batch_size % latents.shape[0] == 0:
                # expand image_latents for batch_size
                deprecation_message = (
                    f"You have passed {batch_size} text prompts (`prompt`), but only {latents.shape[0]} initial"
                    " images (`image`). Initial images are now duplicating to match the number of text prompts. Note"
                    " that this behavior is deprecated and will be removed in a version 1.0.0. Please make sure to update"
                    " your script to pass as many initial images as text prompts to suppress this warning."
                )
                deprecate("len(prompt) != len(image)", "1.0.0", deprecation_message, standard_warn=False)
                additional_latents_per_image = batch_size // latents.shape[0]
                latents = torch.cat([latents] * additional_latents_per_image, dim=0)
            else:
                raise ValueError(
                    f"Cannot duplicate `image` of batch size {latents.shape[0]} to {batch_size} text prompts."
                )
        else:
            latents = torch.cat([latents], dim=0)

        return latents

    def get_epsilon(self, model_output: torch.Tensor, sample: torch.Tensor, timestep: int):
        pred_type = self.inverse_scheduler.config.prediction_type
        alpha_prod_t = self.inverse_scheduler.alphas_cumprod[timestep]

        beta_prod_t = 1 - alpha_prod_t

        if pred_type == "epsilon":
            return model_output
        elif pred_type == "sample":
            return (sample - alpha_prod_t ** (0.5) * model_output) / beta_prod_t ** (0.5)
        elif pred_type == "v_prediction":
            return (alpha_prod_t**0.5) * model_output + (beta_prod_t**0.5) * sample
        else:
            raise ValueError(
                f"prediction_type given as {pred_type} must be one of `epsilon`, `sample`, or `v_prediction`"
            )

    def auto_corr_loss(self, hidden_states, generator=None):
        reg_loss = 0.0
        for i in range(hidden_states.shape[0]):
            for j in range(hidden_states.shape[1]):
                noise = hidden_states[i : i + 1, j : j + 1, :, :]
                while True:
                    roll_amount = torch.randint(noise.shape[2] // 2, (1,), generator=generator).item()
                    reg_loss += (noise * torch.roll(noise, shifts=roll_amount, dims=2)).mean() ** 2
                    reg_loss += (noise * torch.roll(noise, shifts=roll_amount, dims=3)).mean() ** 2

                    if noise.shape[2] <= 8:
                        break
                    noise = F.avg_pool2d(noise, kernel_size=2)
        return reg_loss

    def kl_divergence(self, hidden_states):
        mean = hidden_states.mean()
        var = hidden_states.var()
        return var + mean**2 - 1 - torch.log(var + 1e-7)

    @torch.no_grad()
    @replace_example_docstring(EXAMPLE_DOC_STRING)
    def __call__(
        self,
        prompt: Optional[Union[str, List[str]]] = None,
        source_embeds: torch.Tensor = None,
        target_embeds: torch.Tensor = None,
        height: Optional[int] = None,
        width: Optional[int] = None,
        num_inference_steps: int = 50,
        guidance_scale: float = 7.5,
        negative_prompt: Optional[Union[str, List[str]]] = None,
        num_images_per_prompt: Optional[int] = 1,
        eta: float = 0.0,
        generator: Optional[Union[torch.Generator, List[torch.Generator]]] = None,
        latents: Optional[torch.FloatTensor] = None,
        prompt_embeds: Optional[torch.FloatTensor] = None,
        negative_prompt_embeds: Optional[torch.FloatTensor] = None,
        cross_attention_guidance_amount: float = 0.1,
        output_type: Optional[str] = "pil",
        return_dict: bool = True,
        callback: Optional[Callable[[int, int, torch.FloatTensor], None]] = None,
        callback_steps: Optional[int] = 1,
        cross_attention_kwargs: Optional[Dict[str, Any]] = None,
    ):
        r"""
        Function invoked when calling the pipeline for generation.

        Args:
            prompt (`str` or `List[str]`, *optional*):
                The prompt or prompts to guide the image generation. If not defined, one has to pass `prompt_embeds`.
                instead.
            source_embeds (`torch.Tensor`):
                Source concept embeddings. Generation of the embeddings as per the [original
                paper](https://arxiv.org/abs/2302.03027). Used in discovering the edit direction.
            target_embeds (`torch.Tensor`):
                Target concept embeddings. Generation of the embeddings as per the [original
                paper](https://arxiv.org/abs/2302.03027). Used in discovering the edit direction.
            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_inference_steps (`int`, *optional*, defaults to 50):
                The number of denoising steps. More denoising steps usually lead to a higher quality image at the
                expense of slower inference.
            guidance_scale (`float`, *optional*, defaults to 7.5):
                Guidance scale as defined in [Classifier-Free Diffusion Guidance](https://arxiv.org/abs/2207.12598).
                `guidance_scale` is defined as `w` of equation 2. of [Imagen
                Paper](https://arxiv.org/pdf/2205.11487.pdf). Guidance scale is enabled by setting `guidance_scale >
                1`. Higher guidance scale encourages to generate images that are closely linked to the text `prompt`,
                usually at the expense of lower image quality.
            negative_prompt (`str` or `List[str]`, *optional*):
                The prompt or prompts not to guide the image generation. If not defined, one has to pass
                `negative_prompt_embeds` instead. Ignored when not using guidance (i.e., ignored if `guidance_scale` is
                less than `1`).
            num_images_per_prompt (`int`, *optional*, defaults to 1):
                The number of images to generate per prompt.
            eta (`float`, *optional*, defaults to 0.0):
                Corresponds to parameter eta (η) in the DDIM paper: https://arxiv.org/abs/2010.02502. Only applies to
                [`schedulers.DDIMScheduler`], will be ignored for others.
            generator (`torch.Generator` or `List[torch.Generator]`, *optional*):
                One or a list of [torch generator(s)](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 will ge generated by sampling using the supplied random `generator`.
            prompt_embeds (`torch.FloatTensor`, *optional*):
                Pre-generated text embeddings. Can be used to easily tweak text inputs, *e.g.* prompt weighting. If not
                provided, text embeddings will be generated from `prompt` input argument.
            negative_prompt_embeds (`torch.FloatTensor`, *optional*):
                Pre-generated negative text embeddings. Can be used to easily tweak text inputs, *e.g.* prompt
                weighting. If not provided, negative_prompt_embeds will be generated from `negative_prompt` input
                argument.
            cross_attention_guidance_amount (`float`, defaults to 0.1):
                Amount of guidance needed from the reference cross-attention maps.
            output_type (`str`, *optional*, defaults to `"pil"`):
                The output format of the generate image. Choose between
                [PIL](https://pillow.readthedocs.io/en/stable/): `PIL.Image.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.
            callback (`Callable`, *optional*):
                A function that will be called every `callback_steps` steps during inference. The function will be
                called with the following arguments: `callback(step: int, timestep: int, latents: torch.FloatTensor)`.
            callback_steps (`int`, *optional*, defaults to 1):
                The frequency at which the `callback` function will be called. If not specified, the callback will be
                called at every step.

        Examples:

        Returns:
            [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] or `tuple`:
            [`~pipelines.stable_diffusion.StableDiffusionPipelineOutput`] if `return_dict` is True, otherwise a `tuple.
            When returning a tuple, the first element is a list with the generated images, and the second element is a
            list of `bool`s denoting whether the corresponding generated image likely represents "not-safe-for-work"
            (nsfw) content, according to the `safety_checker`.
        """
        # 0. Define the spatial resolutions.
        height = height or self.unet.config.sample_size * self.vae_scale_factor
        width = width or self.unet.config.sample_size * self.vae_scale_factor

        # 1. Check inputs. Raise error if not correct
        self.check_inputs(
            prompt,
            source_embeds,
            target_embeds,
            callback_steps,
            prompt_embeds,
        )

        # 3. Define call parameters
        if prompt is not None and isinstance(prompt, str):
            batch_size = 1
        elif prompt is not None and isinstance(prompt, list):
            batch_size = len(prompt)
        else:
            batch_size = prompt_embeds.shape[0]
        if cross_attention_kwargs is None:
            cross_attention_kwargs = {}

        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 = guidance_scale > 1.0

        # 3. Encode input prompt
        prompt_embeds, negative_prompt_embeds = self.encode_prompt(
            prompt,
            device,
            num_images_per_prompt,
            do_classifier_free_guidance,
            negative_prompt,
            prompt_embeds=prompt_embeds,
            negative_prompt_embeds=negative_prompt_embeds,
        )
        # 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
        if do_classifier_free_guidance:
            prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds])

        # 4. Prepare timesteps
        self.scheduler.set_timesteps(num_inference_steps, device=device)
        timesteps = self.scheduler.timesteps

        # 5. Generate the inverted noise from the input image or any other image
        # generated from the input prompt.
        num_channels_latents = self.unet.config.in_channels
        latents = self.prepare_latents(
            batch_size * num_images_per_prompt,
            num_channels_latents,
            height,
            width,
            prompt_embeds.dtype,
            device,
            generator,
            latents,
        )
        latents_init = latents.clone()

        # 6. Prepare extra step kwargs. TODO: Logic should ideally just be moved out of the pipeline
        extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)

        # 8. Rejig the UNet so that we can obtain the cross-attenion maps and
        # use them for guiding the subsequent image generation.
        self.unet = prepare_unet(self.unet)

        # 7. Denoising loop where we obtain the cross-attention maps.
        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):
                # expand the latents if we are doing classifier free guidance
                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)

                # predict the noise residual
                noise_pred = self.unet(
                    latent_model_input,
                    t,
                    encoder_hidden_states=prompt_embeds,
                    cross_attention_kwargs={"timestep": t},
                ).sample

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

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

                # call the callback, if provided
                if i == len(timesteps) - 1 or ((i + 1) > num_warmup_steps and (i + 1) % self.scheduler.order == 0):
                    progress_bar.update()
                    if callback is not None and i % callback_steps == 0:
                        callback(i, t, latents)

        # 8. Compute the edit directions.
        edit_direction = self.construct_direction(source_embeds, target_embeds).to(prompt_embeds.device)

        # 9. Edit the prompt embeddings as per the edit directions discovered.
        prompt_embeds_edit = prompt_embeds.clone()
        prompt_embeds_edit[1:2] += edit_direction

        # 10. Second denoising loop to generate the edited image.
        self.scheduler.set_timesteps(num_inference_steps, device=device)
        timesteps = self.scheduler.timesteps

        latents = latents_init
        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):
                # expand the latents if we are doing classifier free guidance
                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)

                # we want to learn the latent such that it steers the generation
                # process towards the edited direction, so make the make initial
                # noise learnable
                x_in = latent_model_input.detach().clone()
                x_in.requires_grad = True

                # optimizer
                opt = torch.optim.SGD([x_in], lr=cross_attention_guidance_amount)

                with torch.enable_grad():
                    # initialize loss
                    loss = Pix2PixZeroL2Loss()

                    # predict the noise residual
                    noise_pred = self.unet(
                        x_in,
                        t,
                        encoder_hidden_states=prompt_embeds_edit.detach(),
                        cross_attention_kwargs={"timestep": t, "loss": loss},
                    ).sample

                    loss.loss.backward(retain_graph=False)
                    opt.step()

                # recompute the noise
                noise_pred = self.unet(
                    x_in.detach(),
                    t,
                    encoder_hidden_states=prompt_embeds_edit,
                    cross_attention_kwargs={"timestep": None},
                ).sample

                latents = x_in.detach().chunk(2)[0]

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

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

                # call the callback, if provided
                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":
            image = self.vae.decode(latents / self.vae.config.scaling_factor, return_dict=False)[0]
            image, has_nsfw_concept = self.run_safety_checker(image, device, prompt_embeds.dtype)
        else:
            image = latents
            has_nsfw_concept = None

        if has_nsfw_concept is None:
            do_denormalize = [True] * image.shape[0]
        else:
            do_denormalize = [not has_nsfw for has_nsfw in has_nsfw_concept]

        image = self.image_processor.postprocess(image, output_type=output_type, do_denormalize=do_denormalize)

        # Offload all models
        self.maybe_free_model_hooks()

        if not return_dict:
            return (image, has_nsfw_concept)

        return StableDiffusionPipelineOutput(images=image, nsfw_content_detected=has_nsfw_concept)

    @torch.no_grad()
    @replace_example_docstring(EXAMPLE_INVERT_DOC_STRING)
    def invert(
        self,
        prompt: Optional[str] = None,
        image: PipelineImageInput = None,
        num_inference_steps: int = 50,
        guidance_scale: float = 1,
        generator: Optional[Union[torch.Generator, List[torch.Generator]]] = None,
        latents: Optional[torch.FloatTensor] = None,
        prompt_embeds: Optional[torch.FloatTensor] = None,
        cross_attention_guidance_amount: float = 0.1,
        output_type: Optional[str] = "pil",
        return_dict: bool = True,
        callback: Optional[Callable[[int, int, torch.FloatTensor], None]] = None,
        callback_steps: Optional[int] = 1,
        cross_attention_kwargs: Optional[Dict[str, Any]] = None,
        lambda_auto_corr: float = 20.0,
        lambda_kl: float = 20.0,
        num_reg_steps: int = 5,
        num_auto_corr_rolls: int = 5,
    ):
        r"""
        Function used to generate inverted latents given a prompt and image.

        Args:
            prompt (`str` or `List[str]`, *optional*):
                The prompt or prompts to guide the image generation. If not defined, one has to pass `prompt_embeds`.
                instead.
            image (`torch.FloatTensor` `np.ndarray`, `PIL.Image.Image`, `List[torch.FloatTensor]`, `List[PIL.Image.Image]`, or `List[np.ndarray]`):
                `Image`, or tensor representing an image batch which will be used for conditioning. Can also accept
                image latents as `image`, if passing latents directly, it will not be encoded again.
            num_inference_steps (`int`, *optional*, defaults to 50):
                The number of denoising steps. More denoising steps usually lead to a higher quality image at the
                expense of slower inference.
            guidance_scale (`float`, *optional*, defaults to 1):
                Guidance scale as defined in [Classifier-Free Diffusion Guidance](https://arxiv.org/abs/2207.12598).
                `guidance_scale` is defined as `w` of equation 2. of [Imagen
                Paper](https://arxiv.org/pdf/2205.11487.pdf). Guidance scale is enabled by setting `guidance_scale >
                1`. Higher guidance scale encourages to generate images that are closely linked to the text `prompt`,
                usually at the expense of lower image quality.
            generator (`torch.Generator` or `List[torch.Generator]`, *optional*):
                One or a list of [torch generator(s)](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 will ge generated by sampling using the supplied random `generator`.
            prompt_embeds (`torch.FloatTensor`, *optional*):
                Pre-generated text embeddings. Can be used to easily tweak text inputs, *e.g.* prompt weighting. If not
                provided, text embeddings will be generated from `prompt` input argument.
            cross_attention_guidance_amount (`float`, defaults to 0.1):
                Amount of guidance needed from the reference cross-attention maps.
            output_type (`str`, *optional*, defaults to `"pil"`):
                The output format of the generate image. Choose between
                [PIL](https://pillow.readthedocs.io/en/stable/): `PIL.Image.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.
            callback (`Callable`, *optional*):
                A function that will be called every `callback_steps` steps during inference. The function will be
                called with the following arguments: `callback(step: int, timestep: int, latents: torch.FloatTensor)`.
            callback_steps (`int`, *optional*, defaults to 1):
                The frequency at which the `callback` function will be called. If not specified, the callback will be
                called at every step.
            lambda_auto_corr (`float`, *optional*, defaults to 20.0):
                Lambda parameter to control auto correction
            lambda_kl (`float`, *optional*, defaults to 20.0):
                Lambda parameter to control Kullback–Leibler divergence output
            num_reg_steps (`int`, *optional*, defaults to 5):
                Number of regularization loss steps
            num_auto_corr_rolls (`int`, *optional*, defaults to 5):
                Number of auto correction roll steps

        Examples:

        Returns:
            [`~pipelines.stable_diffusion.pipeline_stable_diffusion_pix2pix_zero.Pix2PixInversionPipelineOutput`] or
            `tuple`:
            [`~pipelines.stable_diffusion.pipeline_stable_diffusion_pix2pix_zero.Pix2PixInversionPipelineOutput`] if
            `return_dict` is True, otherwise a `tuple. When returning a tuple, the first element is the inverted
            latents tensor and then second is the corresponding decoded image.
        """
        # 1. Define call parameters
        if prompt is not None and isinstance(prompt, str):
            batch_size = 1
        elif prompt is not None and isinstance(prompt, list):
            batch_size = len(prompt)
        else:
            batch_size = prompt_embeds.shape[0]
        if cross_attention_kwargs is None:
            cross_attention_kwargs = {}

        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 = guidance_scale > 1.0

        # 3. Preprocess image
        image = self.image_processor.preprocess(image)

        # 4. Prepare latent variables
        latents = self.prepare_image_latents(image, batch_size, self.vae.dtype, device, generator)

        # 5. Encode input prompt
        num_images_per_prompt = 1
        prompt_embeds, negative_prompt_embeds = self.encode_prompt(
            prompt,
            device,
            num_images_per_prompt,
            do_classifier_free_guidance,
            prompt_embeds=prompt_embeds,
        )
        # 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
        if do_classifier_free_guidance:
            prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds])

        # 4. Prepare timesteps
        self.inverse_scheduler.set_timesteps(num_inference_steps, device=device)
        timesteps = self.inverse_scheduler.timesteps

        # 6. Rejig the UNet so that we can obtain the cross-attenion maps and
        # use them for guiding the subsequent image generation.
        self.unet = prepare_unet(self.unet)

        # 7. Denoising loop where we obtain the cross-attention maps.
        num_warmup_steps = len(timesteps) - num_inference_steps * self.inverse_scheduler.order
        with self.progress_bar(total=num_inference_steps) as progress_bar:
            for i, t in enumerate(timesteps):
                # expand the latents if we are doing classifier free guidance
                latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                latent_model_input = self.inverse_scheduler.scale_model_input(latent_model_input, t)

                # predict the noise residual
                noise_pred = self.unet(
                    latent_model_input,
                    t,
                    encoder_hidden_states=prompt_embeds,
                    cross_attention_kwargs={"timestep": t},
                ).sample

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

                # regularization of the noise prediction
                with torch.enable_grad():
                    for _ in range(num_reg_steps):
                        if lambda_auto_corr > 0:
                            for _ in range(num_auto_corr_rolls):
                                var = torch.autograd.Variable(noise_pred.detach().clone(), requires_grad=True)

                                # Derive epsilon from model output before regularizing to IID standard normal
                                var_epsilon = self.get_epsilon(var, latent_model_input.detach(), t)

                                l_ac = self.auto_corr_loss(var_epsilon, generator=generator)
                                l_ac.backward()

                                grad = var.grad.detach() / num_auto_corr_rolls
                                noise_pred = noise_pred - lambda_auto_corr * grad

                        if lambda_kl > 0:
                            var = torch.autograd.Variable(noise_pred.detach().clone(), requires_grad=True)

                            # Derive epsilon from model output before regularizing to IID standard normal
                            var_epsilon = self.get_epsilon(var, latent_model_input.detach(), t)

                            l_kld = self.kl_divergence(var_epsilon)
                            l_kld.backward()

                            grad = var.grad.detach()
                            noise_pred = noise_pred - lambda_kl * grad

                        noise_pred = noise_pred.detach()

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

                # call the callback, if provided
                if i == len(timesteps) - 1 or (
                    (i + 1) > num_warmup_steps and (i + 1) % self.inverse_scheduler.order == 0
                ):
                    progress_bar.update()
                    if callback is not None and i % callback_steps == 0:
                        callback(i, t, latents)

        inverted_latents = latents.detach().clone()

        # 8. Post-processing
        image = self.vae.decode(latents / self.vae.config.scaling_factor, return_dict=False)[0]
        image = self.image_processor.postprocess(image, output_type=output_type)

        # Offload all models
        self.maybe_free_model_hooks()

        if not return_dict:
            return (inverted_latents, image)

        return Pix2PixInversionPipelineOutput(latents=inverted_latents, images=image)
