pith. machine review for the scientific record. sign in

arxiv: 2605.02222 · v1 · submitted 2026-05-04 · 💻 cs.GR · cs.CV

Recognition: unknown

Generative Modeling with Orbit-Space Particle Flow Matching

Sinan Wang , Jinjin He , Shenyifan Lu , Ruicheng Wang , Greg Turk , Bo Zhu
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:11 UTC · model grok-4.3

classification 💻 cs.GR cs.CV
keywords generative modelingparticle flow matchingorbit space3D shape generationflow matchingpoint cloudssurface normalsShapeNet
0
0 comments X

The pith

Orbit-space canonicalization in particle flow matching lets models generate accurate 3D shapes with up to 5x fewer steps and 26x fewer parameters.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces Orbit-Space Geometric Probability Paths (OGPP) as a flow-matching approach for generative modeling of particle systems that represent shapes. It claims that anonymous particle indexing creates unnecessary variance because particles are identical up to permutation, while their physical embedding allows terminal velocities to carry geometric meaning such as surface normals. By canonicalizing endpoints in orbit space, adding index embeddings to break symmetry, and using arc-length-aware paths, the flows become straighter and more informative. This produces single-step error reductions of two orders of magnitude on minimal-surface tasks and state-of-the-art results on ShapeNet with far fewer inference steps and parameters. A reader would care because the method suggests generative models can respect geometric symmetries and produce differential attributes without extra labels or post-processing.

Core claim

OGPP shows that orbit-space canonicalization of probability-path terminal endpoints, combined with particle index embeddings and geometric paths whose terminal velocities are aware of arc length, reduces per-particle target variance and lets the learned flow encode surface normals as a byproduct, yielding particle generators that match prior accuracy on ShapeNet and minimal surfaces while using 5x fewer steps and up to 26x fewer parameters.

What carries the argument

Orbit-Space Geometric Probability Paths (OGPP), a framework that performs orbit-space canonicalization of flow endpoints, supplies index embeddings for particle specialization, and defines arc-length-aware terminal velocities that generate normals directly from the flow.

If this is right

  • Metric error on minimal-surface benchmarks drops by up to two orders of magnitude after a single inference step.
  • ShapeNet generation reaches state-of-the-art quality using 5 times fewer steps than previous flow-matching methods.
  • Airplane EMD scores become comparable to DiT-3D while using 26 times fewer parameters and 5 times fewer steps.
  • Single-shape encoding produces normals and reconstructions competitive with 6D generators while staying entirely in 3D.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same orbit-space treatment could be applied to other permutation-invariant particle tasks such as molecular conformation generation to test variance reduction outside graphics.
  • Because normals emerge from the flow without supervision, the approach might be extended to predict higher-order geometric fields like mean curvature by redefining the terminal velocity accordingly.
  • If the arc-length conditioning proves robust, the framework could support time-evolving particle systems such as fluid simulations where velocities already carry physical meaning.

Load-bearing premise

The assumption that orbit-space canonicalization plus index embeddings and arc-length-aware velocities will reliably cut target variance and allow the flow to encode normals without added supervision or post-processing.

What would settle it

A single ablation experiment on the minimal-surface benchmarks that removes only the orbit-space canonicalization step and measures whether the one-step metric error reduction falls below one order of magnitude.

Figures

Figures reproduced from arXiv: 2605.02222 by Bo Zhu, Greg Turk, Jinjin He, Ruicheng Wang, Shenyifan Lu, Sinan Wang.

Figure 1
Figure 1. Figure 1: Left: ShapeNet point cloud generation, single-shape encoding on complex Thingi10k meshes with Poisson-reconstructed surfaces, and minimal surface generation. Middle: Generation process visualization showing geometric probability paths transporting noise to surface points with encoded normals. Right: Energy-driven particle generation: diffusion-limited aggregation (top) and multilayer Thomson problem with e… view at source ↗
Figure 2
Figure 2. Figure 2: OGPP. Our framework integrates three key components: (i) orbit￾space canonicalization assigns canonical indices (0,1,2,3) to 𝑋1 while keeping 𝑋0 uncanonicalized, (ii) particle index embeddings (colored blocks) allow each index to specialize to its canonical role, and (iii) geometric probability paths encode surface normals via arc-length-aware terminal velocities. Per￾particle coordinates 𝒙 𝑖 𝑡𝑖 and learna… view at source ↗
Figure 3
Figure 3. Figure 3: Conceptual illustration of the conditional distribution of the ter view at source ↗
Figure 4
Figure 4. Figure 4: Visualization of index-conditioned velocity fields in a realistic minimal-surface configuration (area-constrained). For each strategy, we sample 1000 view at source ↗
Figure 5
Figure 5. Figure 5: Minimal surface generation with variable anchors (3–8). 3- step generation results from a single conditional model trained on varying anchor counts. The generated boundaries appear smooth and accurate across diverse configurations. 4.2 Orbit-Space Canonicalization on 𝑋1 In this subsection we analyze the regression problem and show that orbit-space canonicalization of the terminal endpoint 𝑋1 reduces the co… view at source ↗
Figure 6
Figure 6. Figure 6: Minimal surface generation (3 anchors). We consider the 2D analog of minimal surfaces: soap film boundaries satisfying area constraints. We compare 1-step and 10-step generation results with different methods. Red dots indicate anchor particles; blue dots show generated boundary particles. Our method produces accurate minimal surface boundaries in a single step, while baselines require multiple steps and e… view at source ↗
Figure 7
Figure 7. Figure 7: Illustration of directional cancellation in the Lipschitz ratio. Squares view at source ↗
Figure 8
Figure 8. Figure 8: Geometric probability paths for attribute encoding. Left: Our geometric probability path (quadratic Hermite curve) aligns the terminal tangent with the surface normal 𝒏1, encoding per-particle attributes into the path geometry. Right: Standard linear interpolation leaves the terminal velocity as an unused degree of freedom. tangent aligns with a per-particle attribute. In this work, we instan￾tiate this at… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of terminal velocity magnitude choices. Red dots in view at source ↗
Figure 11
Figure 11. Figure 11: DLA generation comparison. 10-step (left) and 200-step (right) generation results. At 10 steps, baselines produce scattered, non-fractal structures, while ours exhibits realistic dendritic branching. At 200 steps, all methods improve; ours appears closest to the ground-truth fractal morphology. Color encodes particle attachment order (early: dark, late: light). only) in view at source ↗
Figure 12
Figure 12. Figure 12: Uniform blue-noise generation. Comparison of flow-matching variants for 1024-point uniform blue-noise generation. Row 1: One generated point set. Row 2: 2D power spectrum averaged over 1K generated samples. Row 3: Radial power spectrum averaged over 1K generated samples. Row 4: Delaunay triangulation valence (color indicates neighbor count). Our method (5M and 26M) produces the sharpest spectral ring, and… view at source ↗
Figure 13
Figure 13. Figure 13: Quantitative metrics vs. inference steps for all energy-driven tasks. Our method (green) achieves low error from early steps and remains stable, while baselines converge slower and plateau at higher error levels. outperforms the tested baselines, and our 26M model achieves Pear￾son correlation 0.999 and 𝐿2 error 0.014. Figure 13b shows metric evolution across integration steps: our method reaches high Pea… view at source ↗
Figure 14
Figure 14. Figure 14: Adaptive blue-noise generation on CelebA. Unconditionally generated face distributions using our 26M model trained on 200K adaptive blue-noise samples. Point density varies with image intensity, revealing facial features—eyes, nose, mouth, and hair contours—while maintaining local blue-noise spectral characteristics throughout. Adaptive Blue Noise Generation Results. We extend our approach to adaptive blu… view at source ↗
Figure 15
Figure 15. Figure 15: Our generated DLA growth process, rendered as a growing bacterial colony in a Petri dish. view at source ↗
Figure 16
Figure 16. Figure 16: Multilayer Thomson problem generation. Comparison of generated three-shell electron configurations (128 particles per shell). The top row shows the full configuration, and the bottom row zooms into the region indicated by the red box. Red circles mark irregular particle-spacing artifacts that remain in Original FM and Minibatch OT, while EqFM and our method produce Poisson-disk-like particle distributions… view at source ↗
Figure 17
Figure 17. Figure 17: ShapeNet airplane generation. Comparison at 40-step and 200-step inference view at source ↗
Figure 18
Figure 18. Figure 18: ShapeNet car generation. Comparison at 40-step and 200-step inference view at source ↗
Figure 19
Figure 19. Figure 19: ShapeNet chair generation. Comparison at 40-step and 200-step inference. against PCA-estimated normals on the same point cloud. While PCA can recover approximate normal directions, it cannot determine con￾sistent orientations, leading to failures at thin structures like wings and tail fins. The top-left part additionally shows Screened Poisson reconstruction [Kazhdan et al. 2006; Kazhdan and Hoppe 2013] c… view at source ↗
Figure 20
Figure 20. Figure 20: 3D generation with encoded normals on ShapeNet airplane. Green line segments show velocity directions during generation, which converge to surface normals at the terminal frame view at source ↗
Figure 21
Figure 21. Figure 21: 3D generation with encoded normals on ShapeNet airplane. Additional samples demonstrating consistent normal generation across diverse airplane geometries view at source ↗
Figure 22
Figure 22. Figure 22: Normal comparison on ShapeNet airplane. Top-left: Poisson re￾construction from our generated normals. Our method produces consistent, accurate normals compared to PCA-estimated normals. supports high-fidelity reconstructions across this range of geometric complexity. 7.3 Ablation Studies We conduct ablation studies to analyze three key design choices in our framework: (1) orbit-space canonicalization stra… view at source ↗
Figure 23
Figure 23. Figure 23: Single shape encoding. Left: point clouds colored by predicted normals. Right: reconstructed mesh. effectively imposes periodic boundary conditions so that trajectories can wrap across the domain boundary, leads to a slight additional improvement. However, this gain is marginal, we also occasionally observe point pairs that are too close, and such a path may not be equally beneficial for competing methods… view at source ↗
Figure 24
Figure 24. Figure 24: Single-shape encoding comparison on Coral Cuff. Row 1: generated point clouds with zoomed-in details. Row 2: generated point clouds colored by normal direction. Row 3: meshes reconstructed via Screened Poisson. Geometry Distributions (3D) produces sparse, clustered points, while Generalized VP yields noisy normals on thin structures. Geometry Distributions (6D) further requires 6D outputs and higher compu… view at source ↗
Figure 25
Figure 25. Figure 25: Minimal surface (area-constrained) generation ablation study (3 anchors). Comparison of 1-step and 10-step generations; red dots indicate anchor points (conditioning locations), and ground truth (GT) is shown on the right. Without per-particle index (identity) embeddings, our method has only similar expressive power to vanilla Flow Matching (Eulerian view), while equipping vanilla Flow Matching with parti… view at source ↗
Figure 26
Figure 26. Figure 26: Ablation study on canonicalization strategies and initial noise distributions. Row 1: generated point sets. Row 2: averaged 2D power spectrum. Row 3: radial power spectrum compared to ground truth. Red boxes highlight point pairs that are too close to each other view at source ↗
Figure 28
Figure 28. Figure 28: Mid-time analysis of Lipschitz ratios and directional cancellation. From left to right: median and 90th percentile Lipschitz ratio, median and 90th percentile cancellation score at 𝑡 = 1/2 over 𝑘-NN edges (bins ordered by distance). Lower 𝐿𝑖 𝑗 and higher 𝑠canc are better. Canonicalizing 𝑋1 only (“sort 𝑥1”, Ours) yields the lowest Lipschitz ratios and highest cancellation scores, matching our directional-c… view at source ↗
read the original abstract

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. It addresses permutation symmetries via orbit-space canonicalization of terminal endpoints, incorporates particle index embeddings for role specialization, and defines geometric probability paths with arc-length-aware terminal velocities intended to encode geometric attributes such as surface normals as a byproduct. Evaluations claim up to two orders of magnitude metric error reduction on minimal-surface benchmarks in a single inference step, state-of-the-art matching on ShapeNet with 5x fewer steps, airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps, and competitive normals/reconstructions on single-shape encoding while operating in 3D.

Significance. If the central claims hold under verification, the work could meaningfully advance efficient generative modeling for 3D point clouds and surfaces in computer graphics by exploiting symmetries to lower target variance and leveraging physical terminal velocities for implicit geometry capture, potentially enabling lower-parameter, fewer-step inference without post-processing or extra supervision.

major comments (2)
  1. [geometric probability paths component] The performance claims (two-order error reduction on minimal surfaces; competitive normals on single-shape encoding) depend on the arc-length-aware terminal velocities in the geometric probability paths reliably encoding surface normals without supervision. No derivation is supplied showing that the velocity vector at t=1 is forced to align with the surface normal rather than merely defining scalar speed along a position-only path; if the latter, observed normal quality could arise from benchmark-specific design rather than the flow itself. This assumption is load-bearing for the central claims and requires either a mathematical argument or targeted ablation (e.g., comparing velocity alignment metrics with and without the arc-length term).
  2. [method and results] The abstract and method description report large quantitative gains (e.g., 5x fewer steps on ShapeNet, 26x fewer parameters vs. DiT-3D) but supply no equations for the orbit-space canonicalization, index embeddings, or arc-length terminal velocity construction, nor training details or error bars. This makes it impossible to verify whether the three components jointly reduce per-particle variance as asserted or whether results are reproducible; the results section must include these to substantiate the efficiency and accuracy improvements.
minor comments (2)
  1. [Abstract] The abstract would benefit from a single key equation or schematic illustrating how orbit-space canonicalization interacts with the probability path to reduce variance.
  2. [Notation and preliminaries] Notation for particle indices, orbit representatives, and terminal velocities should be introduced once and used consistently to avoid reader confusion in the technical sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the presentation of our work. We provide point-by-point responses below and indicate the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [geometric probability paths component] The performance claims (two-order error reduction on minimal surfaces; competitive normals on single-shape encoding) depend on the arc-length-aware terminal velocities in the geometric probability paths reliably encoding surface normals without supervision. No derivation is supplied showing that the velocity vector at t=1 is forced to align with the surface normal rather than merely defining scalar speed along a position-only path; if the latter, observed normal quality could arise from benchmark-specific design rather than the flow itself. This assumption is load-bearing for the central claims and requires either a mathematical argument or targeted ablation (e.g., comparing velocity alignment metrics with and without the arc-length term).

    Authors: We agree that a formal derivation is necessary to substantiate the claim that the arc-length-aware terminal velocities encode surface normals as a byproduct. The manuscript's description of geometric probability paths is intended to ensure that the terminal velocity aligns with the normal due to the arc-length parameterization, but we acknowledge the lack of explicit proof. In the revised manuscript, we will include a mathematical derivation demonstrating the alignment and add an ablation study on velocity alignment metrics with and without the arc-length term to address this concern. revision: yes

  2. Referee: [method and results] The abstract and method description report large quantitative gains (e.g., 5x fewer steps on ShapeNet, 26x fewer parameters vs. DiT-3D) but supply no equations for the orbit-space canonicalization, index embeddings, or arc-length terminal velocity construction, nor training details or error bars. This makes it impossible to verify whether the three components jointly reduce per-particle variance as asserted or whether results are reproducible; the results section must include these to substantiate the efficiency and accuracy improvements.

    Authors: We concur that the current version of the manuscript does not provide the explicit equations or sufficient implementation details. To enable verification and reproducibility, we will revise the method and results sections to include the equations for orbit-space canonicalization, particle index embeddings, and arc-length terminal velocity construction. We will also add training details and error bars computed over multiple runs. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained design choices with empirical validation

full rationale

The paper motivates OGPP via two insights on permutation symmetries and physical interpretability of velocities, then defines three components (orbit-space canonicalization, index embeddings, arc-length-aware paths) as explicit design choices. No equations, fitted parameters, or derivations are shown that reduce by construction to the inputs or to self-citations. Performance claims are presented as empirical results on benchmarks rather than tautological predictions. The framework remains independent of its own outputs; the arc-length construction is a stated modeling decision, not a renaming or self-definition of the target normals.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that particles are defined up to permutation symmetries and that terminal velocities in physical space can carry geometric meaning; no free parameters or invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance
    Explicitly stated as the first motivating insight in the abstract.
  • domain assumption Particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes
    Explicitly stated as the second motivating insight in the abstract.

pith-pipeline@v0.9.0 · 5526 in / 1346 out tokens · 81844 ms · 2026-05-08T02:11:50.689494+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

127 extracted references · 26 canonical work pages · 14 internal anchors

  1. [1]

    2019 , publisher=

    Computational optimal transport: With applications to data science , author=. 2019 , publisher=

    2019

  2. [2]

    Naval research logistics quarterly , volume=

    The Hungarian method for the assignment problem , author=. Naval research logistics quarterly , volume=. 1955 , publisher=

    1955

  3. [3]

    Proceedings of the IEEE/CVF international conference on computer vision , pages=

    3d shape generation and completion through point-voxel diffusion , author=. Proceedings of the IEEE/CVF international conference on computer vision , pages=

  4. [4]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Diffusion probabilistic models for 3d point cloud generation , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  5. [5]

    Advances in Neural Information Processing Systems , volume=

    Lion: Latent point diffusion models for 3d shape generation , author=. Advances in Neural Information Processing Systems , volume=

  6. [6]

    European Conference on Computer Vision , pages=

    Frepolad: Frequency-rectified point latent diffusion for point cloud generation , author=. European Conference on Computer Vision , pages=. 2024 , organization=

    2024

  7. [7]

    SIGGRAPH Asia 2022 conference papers , pages=

    Neural wavelet-domain diffusion for 3d shape generation , author=. SIGGRAPH Asia 2022 conference papers , pages=

    2022

  8. [8]

    ACM Transactions On Graphics (TOG) , volume=

    3dshape2vecset: A 3d shape representation for neural fields and generative diffusion models , author=. ACM Transactions On Graphics (TOG) , volume=. 2023 , publisher=

    2023

  9. [9]

    Advances in neural information processing systems , volume=

    Dit-3d: Exploring plain diffusion transformers for 3d shape generation , author=. Advances in neural information processing systems , volume=

  10. [10]

    International conference on machine learning , pages=

    Learning representations and generative models for 3d point clouds , author=. International conference on machine learning , pages=. 2018 , organization=

    2018

  11. [11]

    Proceedings of the IEEE/CVF international conference on computer vision , pages=

    Pointflow: 3d point cloud generation with continuous normalizing flows , author=. Proceedings of the IEEE/CVF international conference on computer vision , pages=

  12. [12]

    European Conference on Computer Vision , pages=

    Discrete point flow networks for efficient point cloud generation , author=. European Conference on Computer Vision , pages=. 2020 , organization=

    2020

  13. [13]

    Advances in Neural Information Processing Systems , volume=

    Softflow: Probabilistic framework for normalizing flow on manifolds , author=. Advances in Neural Information Processing Systems , volume=

  14. [14]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

    Setvae: Learning hierarchical composition for generative modeling of set-structured data , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

  15. [15]

    European Conference on Computer Vision , pages=

    Learning gradient fields for shape generation , author=. European Conference on Computer Vision , pages=. 2020 , organization=

    2020

  16. [16]

    Improving and generalizing flow-based generative models with minibatch optimal transport

    Improving and generalizing flow-based generative models with minibatch optimal transport , author=. arXiv preprint arXiv:2302.00482 , year=

    work page internal anchor Pith review arXiv

  17. [17]

    arXiv preprint arXiv:2304.14772 , year=

    Multisample flow matching: Straightening flows with minibatch couplings , author=. arXiv preprint arXiv:2304.14772 , year=

    work page arXiv

  18. [18]

    ShapeNet: An Information-Rich 3D Model Repository

    Shapenet: An information-rich 3d model repository , author=. arXiv preprint arXiv:1512.03012 , year=

    work page internal anchor Pith review arXiv

  19. [19]

    Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets

    Stable video diffusion: Scaling latent video diffusion models to large datasets , author=. arXiv preprint arXiv:2311.15127 , year=

    work page internal anchor Pith review arXiv

  20. [20]

    OpenAI Blog , volume=

    Video generation models as world simulators , author=. OpenAI Blog , volume=

  21. [21]

    Hierarchical Text-Conditional Image Generation with CLIP Latents

    Hierarchical text-conditional image generation with clip latents , author=. arXiv preprint arXiv:2204.06125 , volume=

    work page internal anchor Pith review arXiv

  22. [22]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    High-resolution image synthesis with latent diffusion models , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  23. [23]

    ACM SIGGRAPH 2023 Conference Proceedings , pages=

    Iterative -(de) blending: A minimalist deterministic diffusion model , author=. ACM SIGGRAPH 2023 Conference Proceedings , pages=

    2023

  24. [24]

    ACM SIGGRAPH 2024 conference papers , pages=

    Blue noise for diffusion models , author=. ACM SIGGRAPH 2024 conference papers , pages=

    2024

  25. [25]

    Score-Based Generative Modeling through Stochastic Differential Equations

    Score-based generative modeling through stochastic differential equations , author=. arXiv preprint arXiv:2011.13456 , year=

    work page internal anchor Pith review arXiv 2011

  26. [26]

    pseudo-genus

    Thingi10K: A dataset of 10,000 3D-printing models , author=. arXiv preprint arXiv:1605.04797 , year=

    work page arXiv

  27. [27]

    Proceedings of the IEEE international conference on computer vision , pages=

    Deep learning face attributes in the wild , author=. Proceedings of the IEEE international conference on computer vision , pages=

  28. [28]

    European Conference on Computer Vision , pages=

    Convolutional occupancy networks , author=. European Conference on Computer Vision , pages=. 2020 , organization=

    2020

  29. [29]

    Advances in Neural Information Processing Systems , volume=

    3dilg: Irregular latent grids for 3d generative modeling , author=. Advances in Neural Information Processing Systems , volume=

  30. [30]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Fast point cloud generation with straight flows , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  31. [31]

    arXiv preprint arXiv:2509.23822 , year=

    Space group conditional flow matching , author=. arXiv preprint arXiv:2509.23822 , year=

    work page arXiv

  32. [32]

    Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

    Generative pointnet: Deep energy-based learning on unordered point sets for 3d generation, reconstruction and classification , author=. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages=

  33. [33]

    Advances in neural information processing systems , volume=

    Point-voxel cnn for efficient 3d deep learning , author=. Advances in neural information processing systems , volume=

  34. [34]

    Proceedings of the IEEE/CVF international conference on computer vision , pages=

    3d point cloud generative adversarial network based on tree structured graph convolutions , author=. Proceedings of the IEEE/CVF international conference on computer vision , pages=

  35. [35]

    ACM Transactions on Graphics (TOG) , volume=

    SP-GAN: Sphere-guided 3D shape generation and manipulation , author=. ACM Transactions on Graphics (TOG) , volume=. 2021 , publisher=

    2021

  36. [36]

    Auto-Encoding Variational Bayes

    Auto-encoding variational bayes , author=. arXiv preprint arXiv:1312.6114 , year=

    work page internal anchor Pith review arXiv

  37. [37]

    DreamFusion: Text-to-3D using 2D Diffusion

    Dreamfusion: Text-to-3d using 2d diffusion , author=. arXiv preprint arXiv:2209.14988 , year=

    work page internal anchor Pith review arXiv

  38. [38]

    Advances in neural information processing systems , volume=

    Prolificdreamer: High-fidelity and diverse text-to-3d generation with variational score distillation , author=. Advances in neural information processing systems , volume=

  39. [39]

    Generative Human Geometry Distribution

    Generative human geometry distribution , author=. arXiv preprint arXiv:2503.01448 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

  40. [40]

    arXiv preprint arXiv:2512.07459 , year=

    Human Geometry Distribution for 3D Animation Generation , author=. arXiv preprint arXiv:2512.07459 , year=

    work page arXiv

  41. [41]

    1966 , publisher=

    A computer oriented geodetic data base and a new technique in file sequencing , author=. 1966 , publisher=

    1966

  42. [42]

    Hilbert, David , booktitle=

  43. [43]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Point transformer v3: Simpler faster stronger , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  44. [44]

    ACM Transactions on Graphics (TOG) , volume=

    Octformer: Octree-based transformers for 3d point clouds , author=. ACM Transactions on Graphics (TOG) , volume=. 2023 , publisher=

    2023

  45. [45]

    Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

    Flatformer: Flattened window attention for efficient point cloud transformer , author=. Proceedings of the IEEE/CVF conference on computer vision and pattern recognition , pages=

  46. [46]

    ACM Transactions on Graphics (TOG) , volume=

    3D Gaussian Splatting for Real-Time Radiance Field Rendering , author=. ACM Transactions on Graphics (TOG) , volume=. 2023 , publisher=

    2023

  47. [47]

    arXiv preprint arXiv:2405.20283 , year=

    Tetsphere splatting: Representing high-quality geometry with lagrangian volumetric meshes , author=. arXiv preprint arXiv:2405.20283 , year=

    work page arXiv

  48. [48]

    Proceedings Visualization, 2001

    Point set surfaces , author=. Proceedings Visualization, 2001. VIS'01. , pages=. 2001 , organization=

    2001

  49. [49]

    ACM Transactions on Graphics (TOG) , volume=

    A material point method for snow simulation , author=. ACM Transactions on Graphics (TOG) , volume=. 2013 , publisher=

    2013

  50. [50]

    ACM SIGGRAPH Asia 2009 papers , pages=

    Aggregate dynamics for dense crowd simulation , author=. ACM SIGGRAPH Asia 2009 papers , pages=

    2009

  51. [51]

    ACM siggraph 2007 papers , pages=

    Algebraic point set surfaces , author=. ACM siggraph 2007 papers , pages=

    2007

  52. [52]

    Advances in Neural Information Processing Systems , volume=

    Shape as points: A differentiable poisson solver , author=. Advances in Neural Information Processing Systems , volume=

  53. [53]

    ACM Transactions on Graphics (TOG) , volume=

    The affine particle-in-cell method , author=. ACM Transactions on Graphics (TOG) , volume=. 2015 , publisher=

    2015

  54. [54]

    Journal of Visual Communication and Image Representation , volume=

    Position based dynamics , author=. Journal of Visual Communication and Image Representation , volume=. 2007 , publisher=

    2007

  55. [55]

    , author=

    PLEdestrians: A Least-Effort Approach to Crowd Simulation. , author=. Symposium on computer animation , pages=

  56. [56]

    International Journal of Computer & Information Sciences , volume=

    Two algorithms for constructing a Delaunay triangulation , author=. International Journal of Computer & Information Sciences , volume=. 1980 , publisher=

    1980

  57. [57]

    Computer Methods in Applied Mechanics and Engineering , volume=

    A feature-aware SPH for isotropic unstructured mesh generation , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2021 , publisher=

    2021

  58. [58]

    Computer Methods in Applied Mechanics and Engineering , volume=

    An isotropic unstructured mesh generation method based on a fluid relaxation analogy , author=. Computer Methods in Applied Mechanics and Engineering , volume=. 2019 , publisher=

    2019

  59. [59]

    ACM computing surveys (CSUR) , volume=

    Voronoi diagrams—a survey of a fundamental geometric data structure , author=. ACM computing surveys (CSUR) , volume=. 1991 , publisher=

    1991

  60. [60]

    Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation , pages=

    Particle-based fluid simulation for interactive applications , author=. Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation , pages=

    2003

  61. [61]

    Proceedings of the 28th annual conference on Computer graphics and interactive techniques , pages=

    Procedural modeling of cities , author=. Proceedings of the 28th annual conference on Computer graphics and interactive techniques , pages=

  62. [62]

    ACM SIGGRAPH 2008 papers , pages=

    Interactive procedural street modeling , author=. ACM SIGGRAPH 2008 papers , pages=

    2008

  63. [63]

    2010 , url =

    Amit Patel , title =. 2010 , url =

    2010

  64. [64]

    Computer Graphics Forum , volume=

    Sample elimination for generating poisson disk sample sets , author=. Computer Graphics Forum , volume=. 2015 , organization=

    2015

  65. [65]

    Proceedings of the fourth Eurographics symposium on Geometry processing , volume=

    Poisson surface reconstruction , author=. Proceedings of the fourth Eurographics symposium on Geometry processing , volume=

  66. [66]

    ACM Transactions on Graphics (ToG) , volume=

    Screened poisson surface reconstruction , author=. ACM Transactions on Graphics (ToG) , volume=. 2013 , publisher=

    2013

  67. [67]

    ACM Transactions on Graphics (TOG) , volume=

    Screen-space blue-noise diffusion of Monte Carlo sampling error via hierarchical ordering of pixels , author=. ACM Transactions on Graphics (TOG) , volume=. 2020 , publisher=

    2020

  68. [68]

    ACM Transactions on Graphics (TOG) , volume=

    Optimizing dyadic nets , author=. ACM Transactions on Graphics (TOG) , volume=. 2021 , publisher=

    2021

  69. [69]

    Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation , pages=

    Vortex fluid for gaseous phenomena , author=. Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation , pages=

    2005

  70. [70]

    Proceedings of the 14th annual conference on Computer graphics and interactive techniques , pages=

    Flocks, herds and schools: A distributed behavioral model , author=. Proceedings of the 14th annual conference on Computer graphics and interactive techniques , pages=

  71. [71]

    2012 , publisher=

    Crowd simulation , author=. 2012 , publisher=

    2012

  72. [72]

    2011 , publisher=

    Intermolecular and surface forces , author=. 2011 , publisher=

    2011

  73. [73]

    Science , volume=

    Spectral consequences of photoreceptor sampling in the rhesus retina , author=. Science , volume=. 1983 , publisher=

    1983

  74. [74]

    IEEE Proceedings , volume=

    Dithering with blue noise , author=. IEEE Proceedings , volume=

  75. [75]

    ACM Transactions on Graphics (TOG) , volume=

    Stochastic sampling in computer graphics , author=. ACM Transactions on Graphics (TOG) , volume=. 1986 , publisher=

    1986

  76. [76]

    IEEE transactions on information theory , volume=

    Least squares quantization in PCM , author=. IEEE transactions on information theory , volume=. 1982 , publisher=

    1982

  77. [77]

    ACM Transactions on Graphics (TOG) , volume=

    Capacity-constrained point distributions: A variant of Lloyd's method , author=. ACM Transactions on Graphics (TOG) , volume=. 2009 , publisher=

    2009

  78. [78]

    ACM Transactions on Graphics (TOG) , volume=

    Blue noise through optimal transport , author=. ACM Transactions on Graphics (TOG) , volume=. 2012 , publisher=

    2012

  79. [79]

    ACM Transactions on Graphics (TOG) , volume=

    Wasserstein blue noise sampling , author=. ACM Transactions on Graphics (TOG) , volume=. 2017 , publisher=

    2017

  80. [80]

    ACM Transactions on Graphics (TOG) , volume=

    Blue-noise point sampling using kernel density model , author=. ACM Transactions on Graphics (TOG) , volume=. 2011 , publisher=

    2011

Showing first 80 references.