mlsanityData to 14 Oct 2026

FUSE: A Flow-based Mapping Between Shapes

arXiv 2511.13431 ↗First posted 17 Nov 2025cs.CVcited by 3

On the map: Diffusion models → 3D, point cloud and scene generation

Abstract (arXiv)

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures. 3D shapes are represented as the probability distribution induced by a continuous and invertible flow mapping from a fixed anchor distribution. Given a source and a target shape, the composition of the inverse flow (source to anchor) with the forward flow (anchor to target), we map points between the two surfaces. By encoding the shapes with a pointwise task-tailored embedding, this construction provides an invertible and modality-agnostic representation of maps between shapes across point clouds, meshes, signed distance fields (SDFs), and volumetric data. The resulting representation consistently achieves high coverage and accuracy across diverse benchmarks and challenging settings in shape matching. Beyond shape matching, our framework shows promising results in other tasks, including UV mapping and registration of raw point cloud scans of human bodies.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models. Builds on 40 of its 76 references that are in the map. First posted on arXiv 17 Nov 2025.

Builds on

40 of 76 references.

Closest ancestors · 2

Same direction, newest first

  1. 2023Zero-1-to-3: Zero-shot One Image to 3D Object20 Mar
  2. 2022DreamFusion: Text-to-3D using 2D Diffusion29 Sep

Other references · 38

  1. 2020Denoising Diffusion Implicit Modelscited by 9,781
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,689
  4. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  5. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,041
  6. 2019Expressive Body Capture: 3D Hands, Face, and Body from a Single Imagecited by 1,612
  7. 2021CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fieldscited by 370
  8. 20163D Menagerie: Modeling the 3D shape and pose of animalscited by 312
  9. 2024Flow Matching Guide and Codecited by 301
  10. 2022BEHAVE: Dataset and Method for Tracking Human Object Interactionscited by 249
  11. 2021Editing Conditional Radiance Fieldscited by 222
  12. 2020DiffusionNet: Discretization Agnostic Learning on Surfacescited by 164
26 more
  1. 20183D-CODED : 3D Correspondences by Deep Deformationcited by 160
  2. 2021NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Gocited by 81
  3. 2023Unsupervised Learning of Robust Spectral Shape Matchingcited by 57
  4. 2023Diffusion 3D Features (Diff3F): Decorating Untextured Shapes with Distilled Semantic Featurescited by 55
  5. 2021Shape registration in the time of transformerscited by 51
  6. 2020Correspondence Learning via Linearly-invariant Embeddingcited by 48
  7. 2022Non-rigid Point Cloud Registration with Neural Deformation Pyramidcited by 42
  8. 2022Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal datacited by 37
  9. 2022Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimizationcited by 37
  10. 2022Deep Orientation-Aware Functional Maps: Tackling Symmetry Issues in Shape Matchingcited by 36
  11. 20213D Pose Transfer with Correspondence Learning and Mesh Refinementcited by 30
  12. 2018FARM: Functional Automatic Registration Method for 3D Human Bodiescited by 26
  13. 2024Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolationcited by 26
  14. 2022Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transportcited by 24
  15. 2023NICP: Neural ICP for 3D Human Registration at Scalecited by 21
  16. 2022Intrinsic Neural Fields: Learning Functions on Manifoldscited by 20
  17. 2023Understanding and Improving Features Learned in Deep Functional Mapscited by 20
  18. 2022Neural Implicit Surface Evolutioncited by 18
  19. 2023Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matchingcited by 18
  20. 2024Neural Geometry Processing via Spherical Neural Surfacescited by 14
  21. 2023Non-Rigid Shape Registration via Deep Functional Maps Priorcited by 12
  22. 2024Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learningcited by 12
  23. 2023On Unsupervised Partial Shape Correspondencecited by 11
  24. 2022BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapescited by 7
  25. 2023ReMatching: Low-Resolution Representations for Scalable Shape Correspondencecited by 5
  26. 2024Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshingcited by 5

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Ordered Diffusion for 3D Human Registrationcited by 1
  2. 2026DreamUV: Unwrap Artist-like UV by End-to-End Flow Matchingcited by 0
  3. 2026Coarse-to-Fine: A Hybrid Self-Supervised Method for Non-rigid 3D Shape Matchingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 20243D Shape Tokenization via Latent Flow Matching
  2. 2026SGMatch: Semantic-Guided Non-Rigid Shape Matching with Flow Regularization
  3. 2026Hierarchical Flow Matching for 3D Point Cloud Generation
  4. 2024SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation
  5. 2025Repurposing 2D Diffusion Models for 3D Shape Completion
  6. 2026TORA: Topological Representation Alignment for 3D Shape Assembly
  7. 2023Mosaic-SDF for 3D Generative Models
  8. 2025Denoising Functional Maps: Diffusion Models for Shape Correspondence