Velox: Spatial Memory Makes World Models Efficient

1 INTRODUCTION

• Dense chunked generation retains an ever-growing KV context, making later chunks slower even when the current camera overlaps only a small part of the past scene.Video world models use generated history to preserve appearance, geometry, and object state during long rollouts.Source: §1 · p. 1
• Frame-memory methods retrieve past views by camera overlap, but frame-level selection gives every region in a chunk the same context.Warped point-rendering inputs can also require architectural adaptation or fine-tuning, limiting direct reuse of pretrained video generators.Source: §1 · pp. 1–2
• Velox uses historical camera frustum slabs with depth intervals to route each current latent region to geometry-relevant KV blocks at tiled-attention granularity.It obtains current-block depth through recency-priority multiwarp and uses world-space OBB frustum slab overlap to guide routing.Source: §1 · p. 2, Figure 1 · p. 2
• At chunk 48, attention latency falls from approximately 34.2 ms to 7.8 ms (4.36×), and denoising time falls from approximately 7.19 s to 2.96 s (2.43×).Across the 158-case WBench navigation split, Velox remains within 0.15 API-free average points of dense attention and improves the 19-metric overall average from 75.52 to 75.60.Source: §1 · p. 2
• Velox is training-free and combines region-level frustum routing with global-aligned Gilbert KV storage, sparse attention, and asynchronous geometry construction on one H200.The reported implementation reaches its chunk-48 speedups while geometry construction runs asynchronously with denoising.Source: §1 · p. 3
• For well-covered regions, frustum overlap softly modulates each layer’s model-derived block importance; uncovered regions retain model-derived routing without geometric bias.Previous-chunk retention and global-aligned Gilbert neighborhoods preserve local motion continuity without a separate cross-chunk seam table.Source: §1 · pp. 2–3

2.1 VIDEO WORLD MODELS AND SPATIAL MEMORY

• Video world models and spatial-memory methods extend visual priors to persistent, controllable worlds, making history management central to balancing consistency with dense-attention cost.Spatial memory methods retrieve views, preserve revisits, or expand reconstructed worlds; Velox uses memory to route pretrained attention rather than adding a conditioning pathway or retrained memory module.Source: §2.1 · p. 3

2.2 EFFICIENT ATTENTION AND CONTEXT ROUTING

• Long-context methods reduce attention cost through sparsity, locality, compression, state reuse, selection, or eviction, while video accelerators exploit spatial and temporal regularities.Velox connects these approaches with frame-memory methods by using projective correspondence as a soft prior for region-specific routes, with model-derived fallback and temporal safeguards.Source: §2.2 · p. 3

3 METHOD

• Velox preserves the pretrained generator and conditioning interface, changing only inference-time visibility between current query blocks and historical KV blocks.It represents history with camera frustum slabs and uses their overlap as a soft prior over each layer’s model-derived block importance.Source: §3 · pp. 3–4

3.1 PRELIMINARIES: CHUNKED WORLD GENERATION

• Fixed-size query and KV blocks match FlashAttention-style tiles, letting Velox skip whole historical tiles while keeping block-contiguous gathers.Unlike token-level or variable-size sparsity, fixed routes avoid irregular row-wise indexing.Source: §3.1 · p. 4

3.2 FRUSTUM SLAB CORRESPONDENCE

• Historical blocks become camera frustum slabs with depth intervals, and current query depth comes from recency-priority multiwarp.Valid depth samples are grouped by global Gilbert block; the newest cached frame meeting the sample floor supplies a token’s median depth, with model-derived routing available when no frame qualifies.Source: §3.2 · pp. 4–5

3.3 VELOX ATTENTION FROM FRUSTUM SLAB CORRESPONDENCE

• For well-covered blocks, slab overlap modulates each layer’s model-derived importance; uncovered blocks keep that distribution unchanged.The route also reserves previous-chunk blocks and adds spatial-neighbor and optional reference-block safeguards outside the route budget.Source: §3.3 · p. 6
• Global-aligned Gilbert ordering keeps neighboring regions close in memory and supports block-contiguous KV storage, while the soft route is independent of the space-filling curve.The layout reduces per-call permutation overhead.Source: §3.3 · p. 7

3.4 COMPLEXITY AND DESIGN RATIONALE

• Velox retains visual memory as history grows but caps each query’s exposed route, bounding the historical attention term with fixed route and safeguard budgets.Skipping a block removes both its QK tile product and KV tile load, reducing traffic when attention is memory-bound and tile products when compute-bound.Source: §3.4 · p. 7

4.1 IMPLEMENTATION DETAILS

• The evaluation instantiates Velox on LingBot-Fast-Cam with recency-priority multiwarp, world-space OBB frustum slab IoU, and global-aligned Gilbert KV storage.The reported quality protocol covers all 158 WBench navigation cases; its API-free average excludes VLM-scored setting metrics to allow comparison across judge backends.Source: §4.1 · pp. 7–8

4.2 ATTENTION SCALING OVER 48 CHUNKS

• At chunk 48, attention latency falls from approximately 34.2 ms to 7.8 ms (4.36×), while denoising time falls from approximately 7.19 s to 2.96 s (2.43×).Velox remains nearly flat as retained context grows because each query block receives a bounded route; geometry construction runs asynchronously on the same H200.Source: §4.2 · p. 8, Figure 3 · p. 8

4.3 COMPARISON ON WBENCH

• Velox stays within 0.15 API-free points of dense attention and raises the 19-metric overall average from 75.52 to 75.60 on WBench’s 158 cases.Against model-only block-sparse routing, it raises the API-free average from 73.11 to 73.51, the overall average from 75.01 to 75.60, and spatial consistency from 71.8 to 74.3.Source: §4.3 · p. 8, Table 1 · p. 9

4.4 GEOMETRY AND MODEL-IMPORTANCE AGREEMENT

• At τ = 0.1, layer 14 reaches Rgeo = 0.7302 and R50 = 0.8909, above the random expectation.In a separate calibration, λ = 2 and gref = 0.2 raise fused top-80 positive-overlap recall from 0.602 to 0.852 while changing 9.0% of selected blocks.Source: §4.4 · p. 9, Table 2 · p. 9

4.5 QUALITATIVE COMPARISON

• In the illustrated rollouts, Velox stays close to the input frame while dense attention increasingly drifts in later frames.Examples include room replacement, fading figurine colors, degraded paths, and artifacts across dunes; the cases are illustrative rather than aggregate-quality evidence.Source: §4.5 · p. 9, Figure 4 · p. 10

5 CONCLUSION

• Velox is a training-free router that uses frustum slab overlap to modulate layer-specific block importance while retaining model-derived fallback and local temporal safeguards.At chunk 48, it accelerates attention by 4.36× and denoising by 2.43×; across 158 WBench navigation cases, it remains within 0.15 API-free average points of dense LingBot-Fast-Cam and slightly improves the 19-metric overall average.Source: §5 · p. 10

A.1 SOFT-FUSION CALIBRATION

• λ = 2 and gref = 0.2 raise positive-overlap recall from 0.602 to 0.852 while changing 9.0% of selected blocks.The calibration spans 48 grids; this pair is the weakest tested setting to recover at least 85% of positive-overlap blocks in the fused top-80 while changing at most 25% of model-only selections.Source: §A.1 · p. 16

A.2 ADDITIONAL QUALITATIVE COMPARISONS

• Across beach, subway, and gnome cases, Velox preserves more input-frame detail while dense attention smears textures, loses the crowd, or turns a path into a puddle.In the gnome case, both models eventually enter a tunnel of roots; Velox keeps the cobblestone path and arch along the way.Source: §A.2 · p. 16, Figure 5 · p. 16

• Velox is instantiated on the LingBot-Fast-Cam inference stack with a Wan-style video diffusion transformer.Source: B EXPERIMENTAL IMPLEMENTATION DETAILS · p. 17
• Stored chunks provide source-camera token rectangles and robust depth intervals, while target query blocks obtain Q-depth through multiwarp.Source: B EXPERIMENTAL IMPLEMENTATION DETAILS · p. 17
• Equation (7) supplies the world-space OBB overlap score used for frustum slab matching.Source: B EXPERIMENTAL IMPLEMENTATION DETAILS · p. 17

B.1 REPORTED ROUTING CONFIGURATION

• For rows below the coverage threshold, Velox retains the model-only cumulative-mass route, capped at Kunc = 150; the previous chunk and geometric or temporal safeguards are also included.For covered rows, the fixed fusion uses λ = 2, gref = 0.2, τ = 0.1, and Kcov = 80; the previous chunk is reserved within these budgets.Source: §B.1 · p. 17

B.2 CAMERA POSE ALIGNMENT FOR FRUSTUM SLAB GEOMETRY

• Target ViPE cameras are mapped into the LingBot-map reconstruction frame before multiwarp, OBB construction, frustum slab IoU, and coverage estimation.The latest matched pose pair anchors the alignment, which preserves target-camera relative rotation and scaled translation.Source: §B.2 · p. 17
• Historical slab cameras are refreshed under the current alignment bridge so cached geometry and target queries share one coordinate frame.Source: §B.2 · p. 17

B.3 RECENCY-PRIORITY MULTIWARP FOR QUERY-BLOCK DEPTH

• Multiwarp selects the newest cached frame with enough samples for each target token, avoiding mixed-surface depth statistics; unsupported tokens remain invalid and can use model-derived routing.The bounded cache retains first- and last-frame depths from recent chunks, and query-block depth intervals are formed from valid token depths.Source: §B.3 · pp. 17–18

B.4 RUNTIME PATH AND TIMING SCOPE

• Timing traces report per-chunk attention latency and denoising critical-path time on one H200, while the sparse path uses a native Triton indexed block-sparse kernel.The reported path stores KV caches directly in global-aligned Gilbert order for contiguous tile loads.Source: §B.4 · pp. 18–19

C ASYNCHRONOUS FRUSTUM SLAB CONSTRUCTION

• A worker prepares geometry with a two-chunk freshness lag while denoising proceeds; the main stream waits on a device-side event only when needed.The async worker and denoiser share one H200, and chunks before a Velox state is available run dense attention.Source: C ASYNCHRONOUS FRUSTUM SLAB CONSTRUCTION · p. 19

D VELOX ATTENTION KERNEL AND GLOBAL GILBERT LAYOUT

• Global-aligned Gilbert ordering preserves spatial locality across chunk boundaries, and KV storage follows that order so routed blocks align with contiguous cache ranges.Parity-dependent reflection makes chunk-wise construction match the full-sequence curve; the implementation front-pads chunk slots to align global block ids.Source: Figure 6 · p. 20, §D.2 · p. 20, Figure 7 · p. 21

D.3 INDEXED SPARSE ATTENTION KERNEL

• The indexed kernel computes attention over each query block’s routed KV list, using online softmax normalization and a runtime route-length bound to avoid history-dependent recompilation.Reported timings use the contiguous Gilbert-storage path.Source: §D.3 · p. 21

D.4 ROUTE MATERIALIZATION AND CACHES

• Route materialization reserves the previous chunk, ranks covered rows by fused importance, and gives uncovered rows a capped model-only route with neighborhood safeguards.Source: §D.4 · pp. 21–22

D.5 FAILURE MODES AND VALIDATION SCOPE

• Geometry errors or stale disocclusion depth can promote misleading history; proposed comparisons against random, recent-window, frame/FOV, and model-derived routes isolate geometry’s routing contribution.The implementation limits geometric fusion to well-covered rows while retaining model distributions and previous-chunk and local-neighbor safeguards.Source: §D.5 · p. 22
• Spatial and photometric consistency improve over dense attention, while perspective and subject consistency decrease.Source: §D.5 · p. 22