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MeshOctave generates meshes via cascading resolution transitions

Junkai Lin, Tianhao Zhao, Hang Long, Huipeng Guo, Jielei Zhang, Youjia Zhang, Jiale Xu, Wenbing Li, Rendong Liang, Jozef Hladký, Matthias Nießner, Yuanming Hu, Wei Yang

arXiv:2609.38985v1cs.CV

TL;DR

Mesh generation with explicit topology faces sequential decoding costs or connectivity determined by heuristic or single-scale methods, while existing next-scale mesh hierarchies still rely on sequential local operations. MeshOctave defines scales by dyadic spatial resolution and learns parallel split-and-rewire transitions with discrete diffusion. It outperforms strong baselines across reported metrics and also supports adaptive refinement and mesh subdivision.

  • Problem

    Explicit-topology mesh generation either incurs sequential autoregressive costs or uses continuous representations with heuristic connectivity, while existing next-scale mesh hierarchies rely on sequential local operations.

    Source: §1 · p. 2

  • Method

    MeshOctave uses dyadic spatial-resolution scales and a masked-uniform discrete diffusion model to predict per-face split-and-rewire configurations in parallel within each scale.

    Source: §1 · p. 2, §3.2 · p. 4

  • Results

    MeshOctave outperforms autoregressive, next-scale, and flow-matching baselines across every reported metric.

    Source: §5.1 · p. 7

  • Takeaways & Limitations

    MeshOctave adaptively predicts child occupancy and connectivity for subdivision, modifying topology and concentrating faces on complex regions.

    Source: §5.4 · p. 9

    Sequential generation across scales has higher latency than single-scale flow matching and risks propagating coarse topological errors without backtracking.

    Source: §6 · p. 9

Abstract

from arXiv · show

Generating compact, artist-style meshes with explicit topology typically relies on autoregressive models which incur prohibitive sequential per-token costs, or continuous flow models that depend on heuristic connectivity decoders. Next-scale generation paradigms offer a compelling alternative by enabling parallel intra-scale token prediction and coarse-to-fine refinement from global structure to local topology; yet, existing methods derive hierarchical scales via progressive mesh simplification and invert them sequentially. This eliminates intra-scale parallelism and scales generation steps linearly with face count. In this paper, we propose MeshOctave, which instead defines scale through dyadic spatial grid resolutions, framing coarsening as a deterministic collapse that merges vertices sharing a voxel cell and inherits connectivity. Its inverse operation, split-and-rewire, determines which octant sub-vertices are instantiated for each coarse face and resolves local connectivity using discrete structural tokens. These per-face operations require no serialization, each scale transition is modeled as an unordered set that adds one bit of coordinate precision, naturally supporting dynamic-length meshes and adaptive resolution refinement. We construct a scale-conditioned masked-uniform discrete diffusion model to learn split-and-rewire operation from resolution collapse hierarchies. MeshOctave outperforms strong baselines in geometric fidelity and topological validity by a non-trivial margin, while supporting adaptive resolution refinement and extending naturally to mesh subdivision tasks.

1 INTRODUCTION

Existing mesh generators either incur sequential token costs or resolve topology at a single scale, while prior next-scale mesh hierarchies also rely on sequential local operations. MeshOctave defines scales by spatial resolution and learns parallel split-and-rewire transitions, reporting improvements over strong baselines.

1 INTRODUCTION

  • Autoregressive mesh generation scales inference latency with face count, while continuous approaches can produce fragile connectivity and monolithic-scale methods must balance global coherence with local fidelity.Continuous methods rely on post-hoc thresholding, and connectivity may be resolved only at the terminal vertex set.Source: §1 · p. 2
  • Existing coarse-to-fine mesh hierarchies use sequential local operations, rather than globally parallel, canonical, and order-agnostic scale transitions.The cited approaches derive their hierarchies from simplification or sequential expansion.Source: §1 · p. 2
  • Resolution collapse merges vertices in the same voxel while inheriting connectivity, and split-and-rewire predicts child occupancy and connectivity through per-face decisions.Each transition adds one bit of coordinate precision per axis; the structural tokens form a dynamically sized set conditioned on the preceding scale.Source: §1 · p. 2
  • A scale-conditioned discrete diffusion model learns split-and-rewire transitions, using masked and uniform noise with an hourglass transformer.Occupancy uses categorical heads; adjacency matrices are predicted row by row with a lightweight autoregressive head.Source: §1 · pp. 2–3
  • MeshOctave outperforms strong autoregressive and flow-matching baselines by a substantial margin while supporting next-scale native mesh generation and adaptive resolution refinement.The model predicts structural tokens in parallel within each scale.Source: §1 · p. 3

2 RELATED WORK

Prior mesh-generation work includes sequential autoregressive models, parallel diffusion and flow methods, and next-scale approaches with different hierarchy and topology strategies. MeshOctave is described as jointly refining vertices and topology through multiscale raw-space masked diffusion.

Autoregressive Mesh Generation

  • Autoregressive methods generate explicit connectivity but retain sequential dependencies at token, vertex, or local-update levels, limiting parallelism as meshes grow more complex.Approaches include vertex reuse, connectivity-aware traversal, block aggregation, hierarchical sequencing, and tree structures.Source: §2 · p. 3

Diffusion-Based Mesh Generation

  • Diffusion and flow methods update multiple elements in parallel, but typically recover target-scale connectivity without conditioning it on an explicit coarser mesh.The reviewed approaches include discrete triangle-soup diffusion and continuous latent representations.Source: §2 · p. 3

Next-Scale Mesh Generation

  • For each parent face, split-and-rewire represents vertex splitting with three 8-bit occupancy vectors and rewiring with three intra-parent and three inter-parent 8 × 8 connectivity matrices.The matrices distinguish connections among children of one parent vertex from connections between children of different parent vertices.Source: Figure 2 · p. 4
  • Prior explicit-mesh next-scale methods use sequences of local operations or generate vertices before topology, whereas MeshOctave predicts split-and-rewire configurations within each scale.The comparison table describes MeshOctave as jointly refining vertices and topology via multiscale raw-space masked diffusion.Source: Table 1 · p. 3, §2 · p. 4

3 VERTEX SPLIT-AND-REWIRE CASCADES

MeshOctave builds a canonical mesh hierarchy by collapsing vertices on dyadic grids, then reconstructs finer levels through face-wise split-and-rewire decisions. These decisions encode child occupancy and connectivity, allowing the mesh to be recovered from a coarse level.

3 VERTEX SPLIT-AND-REWIRE CASCADES

  • Nested quantization grids make each resolution transition a globally parallel coarsening step whose inverse decomposes into local, order-free decisions.The resulting hierarchy is canonical and determined by the initial mesh and spatial grid.Source: §3 · p. 4, §3.1 · p. 4

3.1 RESOLUTION COLLAPSE

  • Resolution collapse halves grid resolution, merges fine vertices mapped to the same coarse voxel, and projects faces while removing duplicates and preserving degenerate faces.The operator acts independently and uniformly across grid voxels in a single pass.Source: §3.1 · p. 4

3.2 FACE-CENTRIC SPLIT-AND-REWIRE CASCADES

  • Split-and-rewire inverts collapse by doubling spatial resolution and recovering which child vertices exist and how they connect.Recording each face's structural tokens during collapse allows recovery from a single voxel at level 0.Source: §3.2 · pp. 4–5
  • The scale-conditioned diffusion generator masks z by timestep, conditions an hourglass Transformer on timestep and scale via adaLN, then predicts occupancy and adjacency with separate heads.Categorical heads predict child occupancy, while an autoregressive MLP decodes row-factorized adjacency matrices.Source: Figure 3 · p. 5
  • Each parent face's nine structural tokens combine three 8-bit child-occupancy vectors with six 8×8 connectivity matrices for intra- and inter-parent edges.The matrices comprise three intra-parent and three inter-parent connectivity matrices.Source: §3.2 · pp. 4–5

4 SCALE ADAPTIVE DISCRETE DIFFUSION

This section models per-face split-and-rewire structure as discrete diffusion conditioned on coarse geometry. A masked-uniform training and propose-and-correct inference design refines occupancy and connectivity tokens across scales.

4 SCALE ADAPTIVE DISCRETE DIFFUSION

  • Each coarse face receives a structural token predicted through discrete diffusion, with occupancy decoded categorically and connectivity rows decoded autoregressively.All eight connectivity rows are treated as one slot for masking or revealing.Source: §4 · p. 5

4.1 MASKED-UNIFORM DISCRETE DIFFUSION.

  • Masked-uniform diffusion corrupts slots independently, training a masked pathway on replaced slots and a uniform-noise pathway across all slots, with confidence loss weighted by λ.The uniform pathway also trains a confidence head to predict whether its slot-level predictions are correct.Source: §4.1 · p. 6
  • At inference, the mask and uniform pathways alternate; confidence-based stochastic remasking lets uncertain slots be revisited while stable structures are progressively committed.The propose-and-correct loop begins from a fully masked sequence.Source: §4.1 · pp. 6–7
  • Table 2 groups methods as autoregressive, flow-matching, or discrete diffusion, and marks coarse-to-fine methods with N.Bold and underlined indicate the best and second-best results, respectively.Source: Table 2 · p. 7

4.2 IMPLEMENTATION.

  • The implementation uses a 624M-parameter hourglass Transformer, trained on 350K Objaverse and Toys4K meshes for seven days on eight H800 GPUs.Training meshes contain up to 15,000 faces.Source: §4.2 · p. 7

5 EXPERIMENTS

The experiments compare MeshOctave with autoregressive, next-scale, and flow-matching baselines, then assess inference latency, qualitative output, design ablations, and mesh subdivision.

5 EXPERIMENTS.

  • The evaluation samples 4,096 surface points per generated and reference mesh, measuring CD-L1, CD-L2, Hausdorff distance, and absolute normal consistency.The test set includes 300 meshes from ObjaverseXL and Toys4K and 200 meshes generated by large-scale 3D models; baselines span three paradigms.Source: §5 · p. 7

5.1 QUANTITATIVE ANALYSIS.

  • MeshOctave outperforms autoregressive, next-scale, and flow-matching baselines across every reported metric.The authors report that it also exceeds the strongest flow models by a non-trivial margin.Source: §5.1 · p. 7
  • ∼8 s per scale and ∼90 s across 10 scales, nearly face-count independent, versus ∼15 minutes for 5k faces for ARMesh and VertexRegen (∼10× speedup).The reported per-scale time uses 20 diffusion steps.Source: §5.1 · pp. 7–8

5.2 QUALITATIVE ANALYSIS.

  • Figure 4 compares final meshes for each input: autoregressive outputs often have broken surfaces, flow-matching outputs oversmooth details, and MeshOctave preserves intricate features and delicate parts.Each row shows an input point cloud and meshes from autoregressive, flow-matching, and diffusion-based methods.Source: Figure 4 · p. 8, §5.2 · p. 8

5.3 ABLATION STUDY.

  • Continuous relaxation collapses topology; mask-only diffusion lacks correction, independent adjacency rows add spurious edges, and 1D RoPE weakens local geometric awareness.Table 3 evaluates these four variants, replacing one component per row.Source: §5.3 · p. 9, Table 3 · p. 9

5.4 APPLICATION.

  • Without retraining, MeshOctave conditions on points sampled from a coarse mesh and adaptively predicts child occupancy and connectivity, concentrating faces on complex regions.Figure 8 shows adaptive refinement of geometry and connectivity for mesh subdivision.Source: §5.4 · p. 9, Figure 8 · p. 9

6 CONCLUSION

MeshOctave uses an order-agnostic, globally parallel split-and-rewire cascade with masked-uniform discrete diffusion. Its scale-by-scale generation has latency and error-propagation tradeoffs that motivate future work on distillation and bidirectional transitions.

6 CONCLUSION

  • MeshOctave is a next-scale native-mesh framework centered on a globally parallel, order-agnostic split-and-rewire cascade.Masked-uniform discrete diffusion predicts intra-scale structural tokens in parallel, avoiding prior multiscale methods’ sequential bottlenecks.Source: §6 · p. 9
  • Sequential generation across scales has higher latency than single-scale flow matching and risks propagating coarse topological errors without backtracking.Source: §6 · p. 9
  • Future work will investigate diffusion distillation for faster inference and bidirectional transitions to revise coarse topology dynamically.Source: §6 · p. 9

AI USE STATEMENT

The authors used ChatGPT only as an editorial aid for English expression, grammar, and clarity. They retain responsibility for the manuscript’s integrity and final content.

AI USE STATEMENT

  • ChatGPT was used exclusively to polish English expression, correct grammar, and enhance clarity.Source: AI USE STATEMENT · p. 10
  • The tool was not involved in data, theory, hypotheses, reasoning, methods, implementation, analysis, or interpretation of findings.Source: AI USE STATEMENT · p. 10
  • The authors examined suggested revisions and assume full responsibility for the manuscript’s integrity and final content.Source: AI USE STATEMENT · p. 10

A.1 DETAILS OF THE SPLIT-AND-REWIRE TOKENIZER

The tokenizer uses fixed octant indexing, occupancy-masked connectivity, and degenerate faces to retain unresolved features in the hierarchy for later refinement.

A.1 DETAILS OF THE SPLIT-AND-REWIRE TOKENIZER

  • Octant-absolute indexing uses fixed child octant IDs, making each connectivity matrix a full, lossless 8 × 8 byte regardless of active-child count.It avoids merging, reordering, or budgeting children.Source: §A.1 · p. 14
  • Occupancy masks the corresponding rows and columns of connectivity matrices, so connectivity tokens do not themselves imply that an octant is occupied.Source: §A.1 · p. 14
  • Unclosed edges and isolated active octants decode as zero-area degenerate faces, preserving a hierarchy placeholder for features the current resolution cannot resolve.The examples are (A, B, B) and (A, A, A), respectively.Source: §A.1 · p. 14

A.2 TRAINING AND INFERENCE ALGORITHMS

Algorithms 1 and 2 present the mask-uniform training step and its corresponding mask→token→token inference loop. The pseudocode is written for one sample, while practical runs batch variable-length face sequences using varlen attention packing.

A.2 TRAINING AND INFERENCE ALGORITHMS

  • Algorithms 1 and 2 specify the mask-uniform training step and corresponding mask→token→token generation loop.The pseudocode is written for a single sample; actual runs batch variable-length face sequences using varlen attention packing.Source: §A.2 · p. 14
  • Practical runs batch variable-length face sequences via varlen attention packing, although the algorithms are written for one sample.Source: §A.2 · p. 14
  • With classifier-free guidance enabled, each fθ call uses conditional and unconditional passes; connectivity argmax decodes rows autoregressively.The two logit sets are linearly interpolated before argmax.Source: §A.2 · p. 14

A.3 GEOMETRY-ANCHORED ROPE ANCHOR TABLE

MeshOctave uses geometry-anchored, orderless per-face tokens and focal loss to model connectivity, then iteratively denoises transitions across spatial resolutions. The appendix illustrates usable intermediate levels of detail and reports faster inference than two autoregressive baselines, with a validity caveat for those baselines above 5k faces.

A.3 GEOMETRY-ANCHORED ROPE ANCHOR TABLE

  • Orderless per-face tokens use RoPE conditioned on 3D voxel coordinates and intra-face role, with vertex or vertex-pair anchors encoding geometry and incidence.Lexicographically sorting parent vertices gives canonical edge pairs across shared faces; coarse tokens remain anchored across their three parent vertices.Source: §A.3 · p. 14

A.4 FOCAL LOSS FOR CONNECTIVITY CLASS IMBALANCE

  • Focal loss down-weights confidently predicted slots and prevents the approximately 92% empty connectivity rows from dominating the gradient.The loss applies to both mask and uniform pathways; γ=0 recovers plain cross-entropy.Source: §A.4 · p. 15

A.5 DENOISING WITHIN A RESOLUTION LEVEL

  • Within a resolution transition, iterative prediction and re-masking improve fragmented initial geometry into a coherent mesh by the final denoising step.Figure 9 shows predictions at selected diffusion steps for a transition from the resolution-32 parent mesh.Source: §A.5 · p. 16, Figure 9 · p. 16

A.6 GENERATION ACROSS RESOLUTIONS

  • Each finer split-and-rewire transition doubles grid resolution, adds geometric detail and connectivity, and builds on the preceding mesh.The sequence provides usable levels of detail, so generation can stop at an intermediate resolution when a coarser mesh suffices.Source: §A.6 · p. 16, Figure 10 · p. 17

A.7 INFERENCE SPEED COMPARISON

  • At comparable mesh complexity, MESHOCTAVE is over an order of magnitude faster than armesh and VertexRegen.Neither baseline was trained beyond 5k faces, and validity is unverified for their 5k–10k outputs; MESHOCTAVE generations are verified throughout the measured range.Source: §A.7 · p. 16, Figure 11 · p. 17
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