# 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
import warnings
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 VaeImageProcessor
from ...loaders import LoraLoaderMixin, TextualInversionLoaderMixin
from ...models import AutoencoderKL, UNet2DConditionModel
from ...models.attention_processor import Attention
from ...schedulers import DDIMScheduler, DDPMScheduler, EulerAncestralDiscreteScheduler, LMSDiscreteScheduler
from ...schedulers.scheduling_ddim_inverse import DDIMInverseScheduler
from ...utils import (
    PIL_INTERPOLATION,
    BaseOutput,
    deprecate,
    is_accelerate_available,
    is_accelerate_version,
    logging,
    randn_tensor,
    replace_example_docstring,
)
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):
    warnings.warn(
        "The preprocess method is deprecated and will be removed in a future version. Please"
        " use VaeImageProcessor.preprocess instead",
        FutureWarning,
    )
    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.
    """
    _optional_components = [
        "safety_checker",
        "feature_extractor",
        "caption_generator",
        "caption_processor",
        "inverse_scheduler",
    ]

    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)

    def enable_model_cpu_offload(self, gpu_id=0):
        r"""
        Offloads all models to CPU using accelerate, reducing memory usage with a low impact on performance. Compared
        to `enable_sequential_cpu_offload`, this method moves one whole model at a time to the GPU when its `forward`
        method is called, and the model remains in GPU until the next model runs. Memory savings are lower than with
        `enable_sequential_cpu_offload`, but performance is much better due to the iterative execution of the `unet`.
        """
        if is_accelerate_available() and is_accelerate_version(">=", "0.17.0.dev0"):
            from accelerate import cpu_offload_with_hook
        else:
            raise ImportError("`enable_model_cpu_offload` requires `accelerate v0.17.0` or higher.")

        device = torch.device(f"cuda:{gpu_id}")

        hook = None
        for cpu_offloaded_model in [self.vae, self.text_encoder, self.unet, self.vae]:
            _, hook = cpu_offload_with_hook(cpu_offloaded_model, device, prev_module_hook=hook)

        if self.safety_checker is not None:
            _, hook = cpu_offload_with_hook(self.safety_checker, device, prev_module_hook=hook)

        # We'll offload the last model manually.
        self.final_offload_hook = hook

    # 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

        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]

        prompt_embeds = prompt_embeds.to(dtype=self.text_encoder.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=self.text_encoder.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)

            # 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
            prompt_embeds = torch.cat([negative_prompt_embeds, prompt_embeds])

        return 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):
        warnings.warn(
            "The decode_latents method is deprecated and will be removed in a future version. Please"
            " use VaeImageProcessor instead",
            FutureWarning,
        )
        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 = 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,
        )

        # 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.
        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 last model to CPU
        if hasattr(self, "final_offload_hook") and self.final_offload_hook is not None:
            self.final_offload_hook.offload()

        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: Union[
            torch.FloatTensor,
            PIL.Image.Image,
            np.ndarray,
            List[torch.FloatTensor],
            List[PIL.Image.Image],
            List[np.ndarray],
        ] = 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 accpet
                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 = self._encode_prompt(
            prompt,
            device,
            num_images_per_prompt,
            do_classifier_free_guidance,
            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 last model to CPU
        if hasattr(self, "final_offload_hook") and self.final_offload_hook is not None:
            self.final_offload_hook.offload()

        if not return_dict:
            return (inverted_latents, image)

        return Pix2PixInversionPipelineOutput(latents=inverted_latents, images=image)
