modules/model.py

import importlib
import inspect
import math
from pathlib import Path
import re
from collections import defaultdict
from typing import List, Optional, Union

import time
import k_diffusion
import numpy as np
import PIL
import torch
import torch.nn as nn
import torch.nn.functional as F
from einops import rearrange
from k_diffusion.external import CompVisDenoiser, CompVisVDenoiser
from modules.prompt_parser import FrozenCLIPEmbedderWithCustomWords
from torch import einsum
from torch.autograd.function import Function

from diffusers import DiffusionPipeline
from diffusers.utils import PIL_INTERPOLATION, is_accelerate_available
from diffusers.utils import logging, randn_tensor

import modules.safe as _
from safetensors.torch import load_file

xformers_available = False
try:
    import xformers

    xformers_available = True
except ImportError:
    pass

EPSILON = 1e-6
exists = lambda val: val is not None
default = lambda val, d: val if exists(val) else d
logger = logging.get_logger(__name__)  # pylint: disable=invalid-name


def get_attention_scores(attn, query, key, attention_mask=None):

    if attn.upcast_attention:
        query = query.float()
        key = key.float()

    attention_scores = torch.baddbmm(
        torch.empty(
            query.shape[0],
            query.shape[1],
            key.shape[1],
            dtype=query.dtype,
            device=query.device,
        ),
        query,
        key.transpose(-1, -2),
        beta=0,
        alpha=attn.scale,
    )

    if attention_mask is not None:
        attention_scores = attention_scores + attention_mask

    if attn.upcast_softmax:
        attention_scores = attention_scores.float()

    return attention_scores


class CrossAttnProcessor(nn.Module):
    def __call__(
        self,
        attn,
        hidden_states,
        encoder_hidden_states=None,
        attention_mask=None,
    ):
        batch_size, sequence_length, _ = hidden_states.shape
        attention_mask = attn.prepare_attention_mask(attention_mask, sequence_length, batch_size=batch_size)

        encoder_states = hidden_states
        is_xattn = False
        if encoder_hidden_states is not None:
            is_xattn = True
            img_state = encoder_hidden_states["img_state"]
            encoder_states = encoder_hidden_states["states"]
            weight_func = encoder_hidden_states["weight_func"]
            sigma = encoder_hidden_states["sigma"]

        query = attn.to_q(hidden_states)
        key = attn.to_k(encoder_states)
        value = attn.to_v(encoder_states)

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

        if is_xattn and isinstance(img_state, dict):
            # use torch.baddbmm method (slow)
            attention_scores = get_attention_scores(attn, query, key, attention_mask)
            w = img_state[sequence_length].to(query.device)
            cross_attention_weight = weight_func(w, sigma, attention_scores)
            attention_scores += torch.repeat_interleave(
                cross_attention_weight, repeats=attn.heads, dim=0
            )

            # calc probs
            attention_probs = attention_scores.softmax(dim=-1)
            attention_probs = attention_probs.to(query.dtype)
            hidden_states = torch.bmm(attention_probs, value)

        elif xformers_available:
            hidden_states = xformers.ops.memory_efficient_attention(
                query.contiguous(),
                key.contiguous(),
                value.contiguous(),
                attn_bias=attention_mask,
            )
            hidden_states = hidden_states.to(query.dtype)

        else:
            q_bucket_size = 512
            k_bucket_size = 1024

            # use flash-attention
            hidden_states = FlashAttentionFunction.apply(
                query.contiguous(),
                key.contiguous(),
                value.contiguous(),
                attention_mask,
                False,
                q_bucket_size,
                k_bucket_size,
            )
            hidden_states = hidden_states.to(query.dtype)

        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 ModelWrapper:
    def __init__(self, model, alphas_cumprod):
        self.model = model
        self.alphas_cumprod = alphas_cumprod

    def apply_model(self, *args, **kwargs):
        if len(args) == 3:
            encoder_hidden_states = args[-1]
            args = args[:2]
        if kwargs.get("cond", None) is not None:
            encoder_hidden_states = kwargs.pop("cond")
        return self.model(
            *args, encoder_hidden_states=encoder_hidden_states, **kwargs
        ).sample


class StableDiffusionPipeline(DiffusionPipeline):

    _optional_components = ["safety_checker", "feature_extractor"]

    def __init__(
        self,
        vae,
        text_encoder,
        tokenizer,
        unet,
        scheduler,
    ):
        super().__init__()

        # get correct sigmas from LMS
        self.register_modules(
            vae=vae,
            text_encoder=text_encoder,
            tokenizer=tokenizer,
            unet=unet,
            scheduler=scheduler,
        )
        self.setup_unet(self.unet)
        self.setup_text_encoder()

    def setup_text_encoder(self, n=1, new_encoder=None):
        if new_encoder is not None:
            self.text_encoder = new_encoder

        self.prompt_parser = FrozenCLIPEmbedderWithCustomWords(self.tokenizer, self.text_encoder)
        self.prompt_parser.CLIP_stop_at_last_layers = n

    def setup_unet(self, unet):
        unet = unet.to(self.device)
        model = ModelWrapper(unet, self.scheduler.alphas_cumprod)
        if self.scheduler.prediction_type == "v_prediction":
            self.k_diffusion_model = CompVisVDenoiser(model)
        else:
            self.k_diffusion_model = CompVisDenoiser(model)

    def get_scheduler(self, scheduler_type: str):
        library = importlib.import_module("k_diffusion")
        sampling = getattr(library, "sampling")
        return getattr(sampling, scheduler_type)

    def encode_sketchs(self, state, scale_ratio=8, g_strength=1.0, text_ids=None):
        uncond, cond = text_ids[0], text_ids[1]

        img_state = []
        if state is None:
            return torch.FloatTensor(0)

        for k, v in state.items():
            if v["map"] is None:
                continue

            v_input = self.tokenizer(
                k,
                max_length=self.tokenizer.model_max_length,
                truncation=True,
                add_special_tokens=False,
            ).input_ids

            dotmap = v["map"] < 255
            out = dotmap.astype(float)
            if v["mask_outsides"]:
                out[out==0] = -1
                
            arr = torch.from_numpy(
                out * float(v["weight"]) * g_strength
            )
            img_state.append((v_input, arr))

        if len(img_state) == 0:
            return torch.FloatTensor(0)

        w_tensors = dict()
        cond = cond.tolist()
        uncond = uncond.tolist()
        for layer in self.unet.down_blocks:
            c = int(len(cond))
            w, h = img_state[0][1].shape
            w_r, h_r = w // scale_ratio, h // scale_ratio

            ret_cond_tensor = torch.zeros((1, int(w_r * h_r), c), dtype=torch.float32)
            ret_uncond_tensor = torch.zeros((1, int(w_r * h_r), c), dtype=torch.float32)

            for v_as_tokens, img_where_color in img_state:
                is_in = 0

                ret = (
                    F.interpolate(
                        img_where_color.unsqueeze(0).unsqueeze(1),
                        scale_factor=1 / scale_ratio,
                        mode="bilinear",
                        align_corners=True,
                    )
                    .squeeze()
                    .reshape(-1, 1)
                    .repeat(1, len(v_as_tokens))
                )

                for idx, tok in enumerate(cond):
                    if cond[idx : idx + len(v_as_tokens)] == v_as_tokens:
                        is_in = 1
                        ret_cond_tensor[0, :, idx : idx + len(v_as_tokens)] += ret

                for idx, tok in enumerate(uncond):
                    if uncond[idx : idx + len(v_as_tokens)] == v_as_tokens:
                        is_in = 1
                        ret_uncond_tensor[0, :, idx : idx + len(v_as_tokens)] += ret

                if not is_in == 1:
                    print(f"tokens {v_as_tokens} not found in text")

            w_tensors[w_r * h_r] = torch.cat([ret_uncond_tensor, ret_cond_tensor])
            scale_ratio *= 2

        return w_tensors

    def enable_attention_slicing(self, slice_size: Optional[Union[str, int]] = "auto"):
        r"""
        Enable sliced attention computation.

        When this option is enabled, the attention module will split the input tensor in slices, to compute attention
        in several steps. This is useful to save some memory in exchange for a small speed decrease.

        Args:
            slice_size (`str` or `int`, *optional*, defaults to `"auto"`):
                When `"auto"`, halves the input to the attention heads, so attention will be computed in two steps. If
                a number is provided, uses as many slices as `attention_head_dim // slice_size`. In this case,
                `attention_head_dim` must be a multiple of `slice_size`.
        """
        if slice_size == "auto":
            # half the attention head size is usually a good trade-off between
            # speed and memory
            slice_size = self.unet.config.attention_head_dim // 2
        self.unet.set_attention_slice(slice_size)

    def disable_attention_slicing(self):
        r"""
        Disable sliced attention computation. If `enable_attention_slicing` was previously invoked, this method will go
        back to computing attention in one step.
        """
        # set slice_size = `None` to disable `attention slicing`
        self.enable_attention_slicing(None)

    def enable_sequential_cpu_offload(self, gpu_id=0):
        r"""
        Offloads all models to CPU using accelerate, significantly reducing memory usage. When called, unet,
        text_encoder, vae and safety checker have their state dicts saved to CPU and then are moved to a
        `torch.device('meta') and loaded to GPU only when their specific submodule has its `forward` method called.
        """
        if is_accelerate_available():
            from accelerate import cpu_offload
        else:
            raise ImportError("Please install accelerate via `pip install accelerate`")

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

        for cpu_offloaded_model in [
            self.unet,
            self.text_encoder,
            self.vae,
            self.safety_checker,
        ]:
            if cpu_offloaded_model is not None:
                cpu_offload(cpu_offloaded_model, device)

    @property
    def _execution_device(self):
        r"""
        Returns the device on which the pipeline's models will be executed. After calling
        `pipeline.enable_sequential_cpu_offload()` the execution device can only be inferred from Accelerate's module
        hooks.
        """
        if self.device != torch.device("meta") or not hasattr(self.unet, "_hf_hook"):
            return self.device
        for module in self.unet.modules():
            if (
                hasattr(module, "_hf_hook")
                and hasattr(module._hf_hook, "execution_device")
                and module._hf_hook.execution_device is not None
            ):
                return torch.device(module._hf_hook.execution_device)
        return self.device

    def decode_latents(self, latents):
        latents = latents.to(self.device, dtype=self.vae.dtype)
        latents = 1 / 0.18215 * latents
        image = self.vae.decode(latents).sample
        image = (image / 2 + 0.5).clamp(0, 1)
        # we always cast to float32 as this does not cause significant overhead and is compatible with bfloa16
        image = image.cpu().permute(0, 2, 3, 1).float().numpy()
        return image

    def check_inputs(self, prompt, height, width, callback_steps):
        if 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)}"
            )

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

        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)}."
            )

    def prepare_latents(
        self,
        batch_size,
        num_channels_latents,
        height,
        width,
        dtype,
        device,
        generator,
        latents=None,
    ):
        shape = (batch_size, num_channels_latents, height // 8, width // 8)
        if latents is None:
            if device.type == "mps":
                # randn does not work reproducibly on mps
                latents = torch.randn(
                    shape, generator=generator, device="cpu", dtype=dtype
                ).to(device)
            else:
                latents = torch.randn(
                    shape, generator=generator, device=device, dtype=dtype
                )
        else:
            # if latents.shape != shape:
            #     raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {shape}")
            latents = latents.to(device)

        # scale the initial noise by the standard deviation required by the scheduler
        return latents

    def preprocess(self, image):
        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 = map(lambda x: x - x % 8, (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

    @torch.no_grad()
    def img2img(
        self,
        prompt: Union[str, List[str]],
        num_inference_steps: int = 50,
        guidance_scale: float = 7.5,
        negative_prompt: Optional[Union[str, List[str]]] = None,
        generator: Optional[torch.Generator] = None,
        image: Optional[torch.FloatTensor] = None,
        output_type: Optional[str] = "pil",
        latents=None,
        strength=1.0,
        pww_state=None,
        pww_attn_weight=1.0,
        sampler_name="",
        sampler_opt={},
        start_time=-1,
        timeout=180,
        scale_ratio=8.0,
    ):
        sampler = self.get_scheduler(sampler_name)
        if image is not None:
            image = self.preprocess(image)
            image = image.to(self.vae.device, dtype=self.vae.dtype)

            init_latents = self.vae.encode(image).latent_dist.sample(generator)
            latents = 0.18215 * init_latents

        # 2. Define call parameters
        batch_size = 1 if isinstance(prompt, str) else len(prompt)
        device = self._execution_device
        latents = latents.to(device, dtype=self.unet.dtype)
        # 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 = True
        if guidance_scale <= 1.0:
            raise ValueError("has to use guidance_scale")

        # 3. Encode input prompt
        text_ids, text_embeddings = self.prompt_parser([negative_prompt, prompt])
        text_embeddings = text_embeddings.to(self.unet.dtype)

        init_timestep = (
            int(num_inference_steps / min(strength, 0.999)) if strength > 0 else 0
        )
        sigmas = self.get_sigmas(init_timestep, sampler_opt).to(
            text_embeddings.device, dtype=text_embeddings.dtype
        )

        t_start = max(init_timestep - num_inference_steps, 0)
        sigma_sched = sigmas[t_start:]

        noise = randn_tensor(
            latents.shape,
            generator=generator,
            device=device,
            dtype=text_embeddings.dtype,
        )
        latents = latents.to(device)
        latents = latents + noise * sigma_sched[0]

        # 5. Prepare latent variables
        self.k_diffusion_model.sigmas = self.k_diffusion_model.sigmas.to(latents.device)
        self.k_diffusion_model.log_sigmas = self.k_diffusion_model.log_sigmas.to(
            latents.device
        )

        img_state = self.encode_sketchs(
            pww_state,
            g_strength=pww_attn_weight,
            text_ids=text_ids,
        )

        def model_fn(x, sigma):

            if start_time > 0 and timeout > 0:
                assert (time.time() - start_time) < timeout, "inference process timed out"

            latent_model_input = torch.cat([x] * 2)
            weight_func = lambda w, sigma, qk: w * math.log(1 + sigma) * qk.max()
            encoder_state = {
                "img_state": img_state,
                "states": text_embeddings,
                "sigma": sigma[0],
                "weight_func": weight_func,
            }

            noise_pred = self.k_diffusion_model(
                latent_model_input, sigma, cond=encoder_state
            )
            noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
            noise_pred = noise_pred_uncond + guidance_scale * (
                noise_pred_text - noise_pred_uncond
            )
            return noise_pred

        sampler_args = self.get_sampler_extra_args_i2i(sigma_sched, sampler)
        latents = sampler(model_fn, latents, **sampler_args)

        # 8. Post-processing
        image = self.decode_latents(latents)

        # 10. Convert to PIL
        if output_type == "pil":
            image = self.numpy_to_pil(image)

        return (image,)

    def get_sigmas(self, steps, params):
        discard_next_to_last_sigma = params.get("discard_next_to_last_sigma", False)
        steps += 1 if discard_next_to_last_sigma else 0

        if params.get("scheduler", None) == "karras":
            sigma_min, sigma_max = (
                self.k_diffusion_model.sigmas[0].item(),
                self.k_diffusion_model.sigmas[-1].item(),
            )
            sigmas = k_diffusion.sampling.get_sigmas_karras(
                n=steps, sigma_min=sigma_min, sigma_max=sigma_max, device=self.device
            )
        else:
            sigmas = self.k_diffusion_model.get_sigmas(steps)

        if discard_next_to_last_sigma:
            sigmas = torch.cat([sigmas[:-2], sigmas[-1:]])

        return sigmas

    # https://github.com/AUTOMATIC1111/stable-diffusion-webui/blob/48a15821de768fea76e66f26df83df3fddf18f4b/modules/sd_samplers.py#L454
    def get_sampler_extra_args_t2i(self, sigmas, eta, steps, func):
        extra_params_kwargs = {}

        if "eta" in inspect.signature(func).parameters:
            extra_params_kwargs["eta"] = eta

        if "sigma_min" in inspect.signature(func).parameters:
            extra_params_kwargs["sigma_min"] = sigmas[0].item()
            extra_params_kwargs["sigma_max"] = sigmas[-1].item()

        if "n" in inspect.signature(func).parameters:
            extra_params_kwargs["n"] = steps
        else:
            extra_params_kwargs["sigmas"] = sigmas

        return extra_params_kwargs

    # https://github.com/AUTOMATIC1111/stable-diffusion-webui/blob/48a15821de768fea76e66f26df83df3fddf18f4b/modules/sd_samplers.py#L454
    def get_sampler_extra_args_i2i(self, sigmas, func):
        extra_params_kwargs = {}

        if "sigma_min" in inspect.signature(func).parameters:
            ## last sigma is zero which isn't allowed by DPM Fast & Adaptive so taking value before last
            extra_params_kwargs["sigma_min"] = sigmas[-2]

        if "sigma_max" in inspect.signature(func).parameters:
            extra_params_kwargs["sigma_max"] = sigmas[0]

        if "n" in inspect.signature(func).parameters:
            extra_params_kwargs["n"] = len(sigmas) - 1

        if "sigma_sched" in inspect.signature(func).parameters:
            extra_params_kwargs["sigma_sched"] = sigmas

        if "sigmas" in inspect.signature(func).parameters:
            extra_params_kwargs["sigmas"] = sigmas

        return extra_params_kwargs

    @torch.no_grad()
    def txt2img(
        self,
        prompt: Union[str, List[str]],
        height: int = 512,
        width: int = 512,
        num_inference_steps: int = 50,
        guidance_scale: float = 7.5,
        negative_prompt: Optional[Union[str, List[str]]] = None,
        eta: float = 0.0,
        generator: Optional[torch.Generator] = None,
        latents: Optional[torch.FloatTensor] = None,
        output_type: Optional[str] = "pil",
        callback_steps: Optional[int] = 1,
        upscale=False,
        upscale_x: float = 2.0,
        upscale_method: str = "bicubic",
        upscale_antialias: bool = False,
        upscale_denoising_strength: int = 0.7,
        pww_state=None,
        pww_attn_weight=1.0,
        sampler_name="",
        sampler_opt={},
        start_time=-1,
        timeout=180,
    ):
        sampler = self.get_scheduler(sampler_name)
        # 1. Check inputs. Raise error if not correct
        self.check_inputs(prompt, height, width, callback_steps)

        # 2. Define call parameters
        batch_size = 1 if isinstance(prompt, str) else len(prompt)
        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 = True
        if guidance_scale <= 1.0:
            raise ValueError("has to use guidance_scale")

        # 3. Encode input prompt
        text_ids, text_embeddings = self.prompt_parser([negative_prompt, prompt])
        text_embeddings = text_embeddings.to(self.unet.dtype)

        # 4. Prepare timesteps
        sigmas = self.get_sigmas(num_inference_steps, sampler_opt).to(
            text_embeddings.device, dtype=text_embeddings.dtype
        )

        # 5. Prepare latent variables
        num_channels_latents = self.unet.in_channels
        latents = self.prepare_latents(
            batch_size,
            num_channels_latents,
            height,
            width,
            text_embeddings.dtype,
            device,
            generator,
            latents,
        )
        latents = latents * sigmas[0]
        self.k_diffusion_model.sigmas = self.k_diffusion_model.sigmas.to(latents.device)
        self.k_diffusion_model.log_sigmas = self.k_diffusion_model.log_sigmas.to(
            latents.device
        )

        img_state = self.encode_sketchs(
            pww_state,
            g_strength=pww_attn_weight,
            text_ids=text_ids,
        )

        def model_fn(x, sigma):

            if start_time > 0 and timeout > 0:
                assert (time.time() - start_time) < timeout, "inference process timed out"

            latent_model_input = torch.cat([x] * 2)
            weight_func = lambda w, sigma, qk: w * math.log(1 + sigma) * qk.max()
            encoder_state = {
                "img_state": img_state,
                "states": text_embeddings,
                "sigma": sigma[0],
                "weight_func": weight_func,
            }

            noise_pred = self.k_diffusion_model(
                latent_model_input, sigma, cond=encoder_state
            )
            noise_pred_uncond, noise_pred_text = noise_pred.chunk(2)
            noise_pred = noise_pred_uncond + guidance_scale * (
                noise_pred_text - noise_pred_uncond
            )
            return noise_pred

        extra_args = self.get_sampler_extra_args_t2i(
            sigmas, eta, num_inference_steps, sampler
        )
        latents = sampler(model_fn, latents, **extra_args)

        if upscale:
            target_height = height * upscale_x
            target_width = width * upscale_x
            vae_scale_factor = 2 ** (len(self.vae.config.block_out_channels) - 1)
            latents = torch.nn.functional.interpolate(
                latents,
                size=(
                    int(target_height // vae_scale_factor),
                    int(target_width // vae_scale_factor),
                ),
                mode=upscale_method,
                antialias=upscale_antialias,
            )
            return self.img2img(
                prompt=prompt,
                num_inference_steps=num_inference_steps,
                guidance_scale=guidance_scale,
                negative_prompt=negative_prompt,
                generator=generator,
                latents=latents,
                strength=upscale_denoising_strength,
                sampler_name=sampler_name,
                sampler_opt=sampler_opt,
                pww_state=None,
                pww_attn_weight=pww_attn_weight / 2,
            )

        # 8. Post-processing
        image = self.decode_latents(latents)

        # 10. Convert to PIL
        if output_type == "pil":
            image = self.numpy_to_pil(image)

        return (image,)


class FlashAttentionFunction(Function):
    @staticmethod
    @torch.no_grad()
    def forward(ctx, q, k, v, mask, causal, q_bucket_size, k_bucket_size):
        """Algorithm 2 in the paper"""

        device = q.device
        max_neg_value = -torch.finfo(q.dtype).max
        qk_len_diff = max(k.shape[-2] - q.shape[-2], 0)

        o = torch.zeros_like(q)
        all_row_sums = torch.zeros((*q.shape[:-1], 1), device=device)
        all_row_maxes = torch.full((*q.shape[:-1], 1), max_neg_value, device=device)

        scale = q.shape[-1] ** -0.5

        if not exists(mask):
            mask = (None,) * math.ceil(q.shape[-2] / q_bucket_size)
        else:
            mask = rearrange(mask, "b n -> b 1 1 n")
            mask = mask.split(q_bucket_size, dim=-1)

        row_splits = zip(
            q.split(q_bucket_size, dim=-2),
            o.split(q_bucket_size, dim=-2),
            mask,
            all_row_sums.split(q_bucket_size, dim=-2),
            all_row_maxes.split(q_bucket_size, dim=-2),
        )

        for ind, (qc, oc, row_mask, row_sums, row_maxes) in enumerate(row_splits):
            q_start_index = ind * q_bucket_size - qk_len_diff

            col_splits = zip(
                k.split(k_bucket_size, dim=-2),
                v.split(k_bucket_size, dim=-2),
            )

            for k_ind, (kc, vc) in enumerate(col_splits):
                k_start_index = k_ind * k_bucket_size

                attn_weights = einsum("... i d, ... j d -> ... i j", qc, kc) * scale

                if exists(row_mask):
                    attn_weights.masked_fill_(~row_mask, max_neg_value)

                if causal and q_start_index < (k_start_index + k_bucket_size - 1):
                    causal_mask = torch.ones(
                        (qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device
                    ).triu(q_start_index - k_start_index + 1)
                    attn_weights.masked_fill_(causal_mask, max_neg_value)

                block_row_maxes = attn_weights.amax(dim=-1, keepdims=True)
                attn_weights -= block_row_maxes
                exp_weights = torch.exp(attn_weights)

                if exists(row_mask):
                    exp_weights.masked_fill_(~row_mask, 0.0)

                block_row_sums = exp_weights.sum(dim=-1, keepdims=True).clamp(
                    min=EPSILON
                )

                new_row_maxes = torch.maximum(block_row_maxes, row_maxes)

                exp_values = einsum("... i j, ... j d -> ... i d", exp_weights, vc)

                exp_row_max_diff = torch.exp(row_maxes - new_row_maxes)
                exp_block_row_max_diff = torch.exp(block_row_maxes - new_row_maxes)

                new_row_sums = (
                    exp_row_max_diff * row_sums
                    + exp_block_row_max_diff * block_row_sums
                )

                oc.mul_((row_sums / new_row_sums) * exp_row_max_diff).add_(
                    (exp_block_row_max_diff / new_row_sums) * exp_values
                )

                row_maxes.copy_(new_row_maxes)
                row_sums.copy_(new_row_sums)

        lse = all_row_sums.log() + all_row_maxes

        ctx.args = (causal, scale, mask, q_bucket_size, k_bucket_size)
        ctx.save_for_backward(q, k, v, o, lse)

        return o

    @staticmethod
    @torch.no_grad()
    def backward(ctx, do):
        """Algorithm 4 in the paper"""

        causal, scale, mask, q_bucket_size, k_bucket_size = ctx.args
        q, k, v, o, lse = ctx.saved_tensors

        device = q.device

        max_neg_value = -torch.finfo(q.dtype).max
        qk_len_diff = max(k.shape[-2] - q.shape[-2], 0)

        dq = torch.zeros_like(q)
        dk = torch.zeros_like(k)
        dv = torch.zeros_like(v)

        row_splits = zip(
            q.split(q_bucket_size, dim=-2),
            o.split(q_bucket_size, dim=-2),
            do.split(q_bucket_size, dim=-2),
            mask,
            lse.split(q_bucket_size, dim=-2),
            dq.split(q_bucket_size, dim=-2),
        )

        for ind, (qc, oc, doc, row_mask, lsec, dqc) in enumerate(row_splits):
            q_start_index = ind * q_bucket_size - qk_len_diff

            col_splits = zip(
                k.split(k_bucket_size, dim=-2),
                v.split(k_bucket_size, dim=-2),
                dk.split(k_bucket_size, dim=-2),
                dv.split(k_bucket_size, dim=-2),
            )

            for k_ind, (kc, vc, dkc, dvc) in enumerate(col_splits):
                k_start_index = k_ind * k_bucket_size

                attn_weights = einsum("... i d, ... j d -> ... i j", qc, kc) * scale

                if causal and q_start_index < (k_start_index + k_bucket_size - 1):
                    causal_mask = torch.ones(
                        (qc.shape[-2], kc.shape[-2]), dtype=torch.bool, device=device
                    ).triu(q_start_index - k_start_index + 1)
                    attn_weights.masked_fill_(causal_mask, max_neg_value)

                p = torch.exp(attn_weights - lsec)

                if exists(row_mask):
                    p.masked_fill_(~row_mask, 0.0)

                dv_chunk = einsum("... i j, ... i d -> ... j d", p, doc)
                dp = einsum("... i d, ... j d -> ... i j", doc, vc)

                D = (doc * oc).sum(dim=-1, keepdims=True)
                ds = p * scale * (dp - D)

                dq_chunk = einsum("... i j, ... j d -> ... i d", ds, kc)
                dk_chunk = einsum("... i j, ... i d -> ... j d", ds, qc)

                dqc.add_(dq_chunk)
                dkc.add_(dk_chunk)
                dvc.add_(dv_chunk)

        return dq, dk, dv, None, None, None, None