mlsanityData to 7 Oct 2026

SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds

arXiv 2006.04604 ↗First posted 8 Jun 2020cs.CV cs.LGcited by 97

Not on the map. Why?

Cited by 30 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match that of the underlying target distribution. In this paper, we propose SoftFlow, a probabilistic framework for training normalizing flows on manifolds. To sidestep the dimension mismatch problem, SoftFlow estimates a conditional distribution of the perturbed input data instead of learning the data distribution directly. We experimentally show that SoftFlow can capture the innate structure of the manifold data and generate high-quality samples unlike the conventional flow-based models. Furthermore, we apply the proposed framework to 3D point clouds to alleviate the difficulty of forming thin structures for flow-based models. The proposed model for 3D point clouds, namely SoftPointFlow, can estimate the distribution of various shapes more accurately and achieves state-of-the-art performance in point cloud generation.

Key facts. Cited by 97 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jun 2020.

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Citing papers per year: 2021: 10; 2022: 23; 2023: 21; 2024: 17; 2025: 19; 2026: 7.

97 papers.

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  1. 2022LION: Latent Point Diffusion Models for 3D Shape Generationcited by 552
  2. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  3. 2022Neural Wavelet-domain Diffusion for 3D Shape Generationcited by 132
  4. 2023DiT-3D: Exploring Plain Diffusion Transformers for 3D Shape Generationcited by 110
  5. 2022SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generationcited by 92
  6. 2021SetVAE: Learning Hierarchical Composition for Generative Modeling of Set-Structured Datacited by 78
  7. 2022Towards Implicit Text-Guided 3D Shape Generationcited by 68
  8. 20223D-LDM: Neural Implicit 3D Shape Generation with Latent Diffusion Modelscited by 67
  9. 2024Advances in 3D Generation: A Surveycited by 62
  10. 2022Fast Point Cloud Generation with Straight Flowscited by 56
  11. 2024Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connectionscited by 47
  12. 2024RangeLDM: Fast Realistic LiDAR Point Cloud Generationcited by 45
38 more
  1. 2023JANA: Jointly Amortized Neural Approximation of Complex Bayesian Modelscited by 41
  2. 2023Controllable Mesh Generation Through Sparse Latent Point Diffusion Modelscited by 40
  3. 2021Learning to design drug-like molecules in three-dimensional space using deep generative modelscited by 37
  4. 2023Sketch and Text Guided Diffusion Model for Colored Point Cloud Generationcited by 36
  5. 2023DiffFacto: Controllable Part-Based 3D Point Cloud Generation with Cross Diffusioncited by 32
  6. 2022Universal approximation property of invertible neural networkscited by 30
  7. 2023Neural Wavelet-domain Diffusion for 3D Shape Generation, Inversion, and Manipulationcited by 27
  8. 2024Wasserstein Flow Matching: Generative modeling over families of distributionscited by 27
  9. 2021iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Codercited by 25
  10. 20233DQD: Generalized Deep 3D Shape Prior via Part-Discretized Diffusion Processcited by 25
  11. 2023AI-Generated Content (AIGC) for Various Data Modalities: A Surveycited by 25
  12. 2023GECCO: Geometrically-Conditioned Point Diffusion Modelscited by 24
  13. 2023Quasi-Monte Carlo for 3D Sliced Wassersteincited by 22
  14. 2021FloMo: Tractable Motion Prediction with Normalizing Flowscited by 21
  15. 2021SP-GAN: Sphere-Guided 3D Shape Generation and Manipulationcited by 21
  16. 2021Noise Conditional Flow Model for Learning the Super-Resolution Spacecited by 19
  17. 2025Not-So-Optimal Transport Flows for 3D Point Cloud Generationcited by 17
  18. 2021Go with the Flows: Mixtures of Normalizing Flows for Point Cloud Generation and Reconstructioncited by 16
  19. 2024PointInfinity: Resolution-Invariant Point Diffusion Modelscited by 15
  20. 2022IL-flOw: Imitation Learning from Observation using Normalizing Flowscited by 12
  21. 2023A Review of Change of Variable Formulas for Generative Modelingcited by 12
  22. 2021Density estimation on low-dimensional manifolds: an inflation-deflation approachcited by 11
  23. 2023Pushing the Limits of 3D Shape Generation at Scalecited by 11
  24. 2023Neural Point Cloud Diffusion for Disentangled 3D Shape and Appearance Generationcited by 11
  25. 2023Humans as Light Bulbs: 3D Human Reconstruction from Thermal Reflectioncited by 10
  26. 2023MVDD: Multi-View Depth Diffusion Modelscited by 10
  27. 2023FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generationcited by 9
  28. 2023Fast Training of Diffusion Transformer with Extreme Masking for 3D Point Clouds Generationcited by 9
  29. 2025PointNSP: Autoregressive 3D Point Cloud Generation with Next-Scale Level-of-Detail Predictioncited by 9
  30. 2021Attention-based Transformation from Latent Features to Point Cloudscited by 8
  31. 2022FS-NCSR: Increasing Diversity of the Super-Resolution Space via Frequency Separation and Noise-Conditioned Normalizing Flowcited by 8
  32. 2022COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependencecited by 8
  33. 2022WarpingGAN: Warping Multiple Uniform Priors for Adversarial 3D Point Cloud Generationcited by 7
  34. 2024Efficient 3D Shape Generation via Diffusion Mamba with Bidirectional SSMscited by 7
  35. 2024Efficient and Scalable Point Cloud Generation with Sparse Point-Voxel Diffusion Modelscited by 7
  36. 2022Denoising Deep Generative Modelscited by 6
  37. 2024Multi-scale Latent Point Consistency Models for 3D Shape Generationcited by 6
  38. 2025Representing 3D Shapes With 64 Latent Vectors for 3D Diffusion Modelscited by 6

50 most cited of 97 All 97 (JSON)