from __future__ import annotations import itertools from dataclasses import dataclass, replace from typing import Callable, NamedTuple import torch def compute_trapezoidal_mask_1d( length: int, ramp_left: int, ramp_right: int, left_starts_from_0: bool = False, ) -> torch.Tensor: """ Generate a 1D trapezoidal blending mask with linear ramps. Args: length: Output length of the mask. ramp_left: Fade-in length on the left. ramp_right: Fade-out length on the right. left_starts_from_0: Whether the ramp starts from 0 or first non-zero value. Useful for temporal tiles where the first tile is causal. Returns: A 1D tensor of shape `(length,)` with values in [0, 1]. """ if length <= 0: raise ValueError("Mask length must be positive.") ramp_left = max(0, min(ramp_left, length)) ramp_right = max(0, min(ramp_right, length)) mask = torch.ones(length) if ramp_left > 0: interval_length = ramp_left + 1 if left_starts_from_0 else ramp_left + 2 fade_in = torch.linspace(0.0, 1.0, interval_length)[:-1] if not left_starts_from_0: fade_in = fade_in[1:] mask[:ramp_left] *= fade_in if ramp_right > 0: fade_out = torch.linspace(1.0, 0.0, steps=ramp_right + 2)[1:-1] mask[-ramp_right:] *= fade_out return mask.clamp_(0, 1) def compute_rectangular_mask_1d( length: int, left_ramp: int, right_ramp: int, ) -> torch.Tensor: """ Generate a 1D rectangular (pulse) mask. Args: length: Output length of the mask. left_ramp: Number of elements at the start of the mask to set to 0. right_ramp: Number of elements at the end of the mask to set to 0. Returns: A 1D tensor of shape `(length,)` with values 0 or 1. """ if length <= 0: raise ValueError("Mask length must be positive.") mask = torch.ones(length) if left_ramp > 0: mask[:left_ramp] = 0 if right_ramp > 0: mask[-right_ramp:] = 0 return mask @dataclass(frozen=True) class DimensionInterval: start: int end: int left_ramp: int right_ramp: int @dataclass(frozen=True) class DimensionIntervals: """Intervals which a single dimension of the latent space is split into. Each interval is defined by its start, end, left ramp, and right ramp. The start and end are the indices of the first and last element (exclusive) in the interval. Ramps are regions of the interval where the value of the mask tensor is interpolated between 0 and 1 for blending with neighboring intervals. The left ramp and right ramp values are the lengths of the left and right ramps. """ intervals: list[DimensionInterval] @dataclass(frozen=True) class LatentIntervals: """Intervals which the latent tensor of given shape is split into. Each dimension of the latent space is split into intervals based on the length along said dimension. """ original_shape: torch.Size dimension_intervals: tuple[DimensionIntervals, ...] # Operation to split a single dimension of the tensor into intervals based on the length along the dimension. SplitOperation = Callable[[int], DimensionIntervals] # Operation to map the intervals in input dimension to slices and masks along a corresponding output dimension. MappingOperation = Callable[[DimensionIntervals], tuple[list[slice], list[torch.Tensor | None]]] def default_split_operation(length: int) -> DimensionIntervals: return DimensionIntervals(intervals=[DimensionInterval(start=0, end=length, left_ramp=0, right_ramp=0)]) DEFAULT_SPLIT_OPERATION: SplitOperation = default_split_operation def default_mapping_operation( _intervals: DimensionIntervals, ) -> tuple[list[slice], list[torch.Tensor | None]]: return [slice(0, None)], [None] DEFAULT_MAPPING_OPERATION: MappingOperation = default_mapping_operation # --------------------------------------------------------------------------- # Split functions # --------------------------------------------------------------------------- def split_by_size(size: int, overlap: int) -> SplitOperation: """Split a dimension into overlapping tiles of a given size. Tiles are sized ``size`` with ``overlap`` shared elements between consecutive tiles. The last tile may be shorter if the dimension doesn't divide evenly. Args: size: Target tile size (in axis units). overlap: Overlap between consecutive tiles. Returns: A split operation that divides a dimension into tiles. """ if size <= 0: raise ValueError(f"size must be > 0, got {size}") if overlap < 0 or overlap >= size: raise ValueError(f"overlap must satisfy 0 <= overlap < size, got overlap={overlap}, size={size}") def split(dimension_size: int) -> DimensionIntervals: if dimension_size <= size: return DEFAULT_SPLIT_OPERATION(dimension_size) amount = (dimension_size + size - 2 * overlap - 1) // (size - overlap) intervals = [ DimensionInterval(start=0, end=size, left_ramp=0, right_ramp=overlap), *( DimensionInterval( start=i * (size - overlap), end=i * (size - overlap) + size, left_ramp=overlap, right_ramp=overlap, ) for i in range(1, amount - 1) ), DimensionInterval( start=(amount - 1) * (size - overlap), end=dimension_size, left_ramp=overlap, right_ramp=0 ), ] return DimensionIntervals(intervals=intervals) return split def split_temporal_causal(size: int, overlap: int) -> SplitOperation: """Split a temporal axis into overlapping tiles with causal handling. Each tile after the first is shifted back by 1 and its left ramp is increased by 1, ensuring causal continuity through the blend ramps. Args: size: Tile size in axis units. overlap: Overlap between tiles in the same units. Returns: Split operation that divides temporal dimension with causal handling. """ non_causal_split = split_by_size(size, overlap) def split(dimension_size: int) -> DimensionIntervals: if dimension_size <= size: return DEFAULT_SPLIT_OPERATION(dimension_size) dim_intervals = non_causal_split(dimension_size) modified_intervals = [dim_intervals.intervals[0]] + [ replace(interval, start=interval.start - 1, left_ramp=interval.left_ramp + 1) for interval in dim_intervals.intervals[1:] ] return DimensionIntervals(intervals=modified_intervals) return split def split_temporal(tile_size_frames: int, overlap_frames: int) -> SplitOperation: """Split a temporal axis in video frame space into overlapping tiles. Args: tile_size_frames: Tile length in frames. overlap_frames: Overlap between consecutive tiles in frames. Returns: Split operation that takes frame count and returns DimensionIntervals in frame indices. """ non_causal_split = split_by_size(tile_size_frames, overlap_frames) def split(dimension_size: int) -> DimensionIntervals: if dimension_size <= tile_size_frames: return DEFAULT_SPLIT_OPERATION(dimension_size) dim_intervals = non_causal_split(dimension_size) modified_intervals = [ replace(interval, end=interval.end + 1, right_ramp=0) for interval in dim_intervals.intervals[:-1] ] + [replace(dim_intervals.intervals[-1], right_ramp=0)] return DimensionIntervals(intervals=modified_intervals) return split def split_by_count_temporal_causal(num_tiles: int, overlap: int = 0) -> SplitOperation: """Split a temporal dimension by count with causal handling. Wraps :func:`split_by_count` with the same causal adjustment as :func:`split_temporal_causal`: each tile after the first is shifted back by 1 and its left ramp is increased by 1. Args: num_tiles: Number of tiles. Must be >= 1. overlap: Overlap between adjacent tiles (default 0). Returns: A split operation that divides a temporal dimension into tiles. """ non_causal_split = split_by_count(num_tiles, overlap) def split(dimension_size: int) -> DimensionIntervals: dim_intervals = non_causal_split(dimension_size) if len(dim_intervals.intervals) <= 1: return dim_intervals modified_intervals = [dim_intervals.intervals[0]] + [ replace(interval, start=interval.start - 1, left_ramp=interval.left_ramp + 1) for interval in dim_intervals.intervals[1:] ] return DimensionIntervals(intervals=modified_intervals) return split def split_by_count(num_tiles: int, overlap: int = 0) -> SplitOperation: """Split a dimension into a given number of tiles with overlap. Computes the tile size as ``(dim_size + overlap * (num_tiles - 1)) // num_tiles`` so that ``num_tiles`` tiles of that size with ``overlap`` shared elements cover the dimension evenly. Delegates to :func:`split_by_size` for the actual interval construction. When the total ``dim_size + overlap * (num_tiles - 1)`` is not evenly divisible by ``num_tiles``, the first ``remainder`` tiles each absorb one extra unit. Args: num_tiles: Number of tiles. Must be >= 1. overlap: Overlap between adjacent tiles (default 0). Must be >= 0 and less than the computed tile size. Returns: A split operation that divides a dimension into tiles. """ if num_tiles < 1: raise ValueError(f"num_tiles must be >= 1, got {num_tiles}") if overlap < 0: raise ValueError(f"overlap must be >= 0, got {overlap}") def split(dim_size: int) -> DimensionIntervals: if num_tiles > dim_size: raise ValueError( f"num_tiles ({num_tiles}) exceeds dim_size ({dim_size}). Cannot assign at least 1 unit per tile." ) if num_tiles == 1: return DEFAULT_SPLIT_OPERATION(dim_size) total = dim_size + overlap * (num_tiles - 1) tile_size = total // num_tiles remainder = total % num_tiles base_intervals = split_by_size(tile_size, overlap)(dim_size - remainder).intervals # First `remainder` tiles each absorb 1 extra unit; shift subsequent boundaries. intervals: list[DimensionInterval] = [] for i, iv in enumerate(base_intervals): shift = min(i, remainder) grow = 1 if i < remainder else 0 intervals.append(replace(iv, start=iv.start + shift, end=iv.end + shift + grow)) return DimensionIntervals(intervals=intervals) return split # --------------------------------------------------------------------------- # Mapping operations # --------------------------------------------------------------------------- def identity_mapping_operation(intervals: DimensionIntervals) -> tuple[list[slice], list[torch.Tensor | None]]: """Map each DimensionInterval to an output region at the same position, with trapezoidal blend masks. For every interval the output start/end matches the input start/end and a 1-D blending mask is built from the interval's left_ramp and right_ramp. """ out_slices: list[slice] = [] masks: list[torch.Tensor | None] = [] for iv in intervals.intervals: out_slices.append(slice(iv.start, iv.end)) masks.append(compute_trapezoidal_mask_1d(iv.end - iv.start, iv.left_ramp, iv.right_ramp)) return out_slices, masks class Tile(NamedTuple): """ Represents a single tile. Attributes: in_coords: Tuple of slices specifying where to cut the tile from the INPUT tensor. out_coords: Tuple of slices specifying where this tile's OUTPUT should be placed in the reconstructed OUTPUT tensor. masks_1d: Per-dimension masks in OUTPUT units. These are used to create all-dimensional blending mask. Methods: blend_mask: Create a single N-D mask from the per-dimension masks. """ in_coords: tuple[slice, ...] out_coords: tuple[slice, ...] masks_1d: tuple[torch.Tensor | None, ...] @property def blend_mask(self) -> torch.Tensor: num_dims = len(self.out_coords) per_dimension_masks: list[torch.Tensor] = [] for dim_idx in range(num_dims): mask_1d = self.masks_1d[dim_idx] view_shape = [1] * num_dims if mask_1d is None: # Broadcast mask along this dimension (length 1). one = torch.ones(1) view_shape[dim_idx] = 1 per_dimension_masks.append(one.view(*view_shape)) continue # Reshape (L,) -> (1, ..., L, ..., 1) so masks across dimensions broadcast-multiply. view_shape[dim_idx] = mask_1d.shape[0] per_dimension_masks.append(mask_1d.view(*view_shape)) # Multiply per-dimension masks to form the full N-D mask (separable blending window). combined_mask = per_dimension_masks[0] for mask in per_dimension_masks[1:]: combined_mask = combined_mask * mask return combined_mask def create_tiles_from_intervals_and_mappers( intervals: LatentIntervals, mappers: list[MappingOperation], ) -> list[Tile]: full_dim_input_slices: list[list[slice]] = [] full_dim_output_slices: list[list[slice]] = [] full_dim_masks_1d: list[list[torch.Tensor | None]] = [] for axis_index in range(len(intervals.original_shape)): dimension_intervals = intervals.dimension_intervals[axis_index] input_slices = [slice(interval.start, interval.end) for interval in dimension_intervals.intervals] output_slices, masks_1d = mappers[axis_index](dimension_intervals) n_intervals = len(input_slices) if len(output_slices) != n_intervals or len(masks_1d) != n_intervals: raise ValueError( f"Axis {axis_index}: mapper produced {len(output_slices)} output slices and " f"{len(masks_1d)} masks for {n_intervals} input intervals" ) full_dim_input_slices.append(input_slices) full_dim_output_slices.append(output_slices) full_dim_masks_1d.append(masks_1d) return [ Tile(in_coords=in_coord, out_coords=out_coord, masks_1d=mask_1d) for in_coord, out_coord, mask_1d in zip( itertools.product(*full_dim_input_slices), itertools.product(*full_dim_output_slices), itertools.product(*full_dim_masks_1d), strict=True, ) ] def create_tiles( latent_shape: torch.Size, splitters: list[SplitOperation], mappers: list[MappingOperation], ) -> list[Tile]: if len(splitters) != len(latent_shape): raise ValueError( f"Number of splitters must be equal to number of dimensions in latent shape, " f"got {len(splitters)} and {len(latent_shape)}" ) if len(mappers) != len(latent_shape): raise ValueError( f"Number of mappers must be equal to number of dimensions in latent shape, " f"got {len(mappers)} and {len(latent_shape)}" ) intervals = [splitter(length) for splitter, length in zip(splitters, latent_shape, strict=True)] latent_intervals = LatentIntervals(original_shape=latent_shape, dimension_intervals=tuple(intervals)) return create_tiles_from_intervals_and_mappers(latent_intervals, mappers) # --------------------------------------------------------------------------- # Video-grid tiling configs # --------------------------------------------------------------------------- @dataclass(frozen=True) class DimensionTilingConfig: """Tiling parameters for a single dimension of the patchified grid. Attributes: num_tiles: Number of tiles along this dimension. overlap: Overlap between adjacent tiles, in latent grid units. Adjacent tiles share ``overlap`` grid cells at their boundary, producing an overlap zone blended with trapezoidal masks. """ num_tiles: int overlap: int = 0 def __post_init__(self) -> None: if self.num_tiles < 1: raise ValueError(f"num_tiles must be >= 1, got {self.num_tiles}") if self.overlap < 0: raise ValueError(f"overlap must be >= 0, got {self.overlap}") @classmethod def from_tile_size(cls, dim_size: int, tile_size: int, overlap: int = 0) -> DimensionTilingConfig: """Create config by computing ``num_tiles`` from dimension size and tile size. Args: dim_size: Total length of the dimension. tile_size: Desired tile size. overlap: Overlap between consecutive tiles. Returns: A ``DimensionTilingConfig`` with the computed ``num_tiles``. """ split_op = split_by_size(tile_size, overlap) intervals = split_op(dim_size) return cls(num_tiles=len(intervals.intervals), overlap=overlap) @dataclass(frozen=True) class TileCountConfig: """Tiling layout for a ``(F, H, W)`` grid. Specifies tile *counts* per dimension (as opposed to tile *sizes* which are used by the single-GPU VAE ``TilingConfig``). Attributes: frames: Tiling along the temporal (frames) dimension. height: Tiling along the latent height dimension. width: Tiling along the latent width dimension. """ frames: DimensionTilingConfig = DimensionTilingConfig(num_tiles=1, overlap=0) height: DimensionTilingConfig = DimensionTilingConfig(num_tiles=1, overlap=0) width: DimensionTilingConfig = DimensionTilingConfig(num_tiles=1, overlap=0)