mlsanityData to 7 Oct 2026

Star-Shaped Denoising Diffusion Probabilistic Models

arXiv 2302.05259 ↗First posted 10 Feb 2023stat.ML cs.LGcited by 13

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Denoising Diffusion Probabilistic Models (DDPMs) provide the foundation for the recent breakthroughs in generative modeling. Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM). Its star-shaped diffusion process allows us to bypass the need to define the transition probabilities or compute posteriors. We establish duality between star-shaped and specific Markovian diffusions for the exponential family of distributions and derive efficient algorithms for training and sampling from SS-DDPMs. In the case of Gaussian distributions, SS-DDPM is equivalent to DDPM. However, SS-DDPMs provide a simple recipe for designing diffusion models with distributions such as Beta, von Misesunicodex2013Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM. Our implementation is available at https://github.com/andrey-okhotin/star-shaped .

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 43 of its 54 references that are in the map. First posted on arXiv 10 Feb 2023.

Builds on

43 of 54 references.

Closest ancestors · 17

Same direction, newest first

  1. 2022Blurring Diffusion Models12 Sep
  2. 2022Soft Diffusion: Score Matching for General Corruptions12 Sep
  3. 2022Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise19 Aug
  4. 2022Riemannian Diffusion Models16 Aug
  5. 2022gDDIM: Generalized denoising diffusion implicit models11 Jun
  6. 2022Maximum Likelihood Training of Implicit Nonlinear Diffusion Models27 May
  7. 2022Riemannian Score-Based Generative Modelling6 Feb
  8. 2021Diffusion Normalizing Flow14 Oct
  9. 2021Denoising Diffusion Gamma Models10 Oct
  10. 2021Structured Denoising Diffusion Models in Discrete State-Spaces7 Jul
  11. 2021Variational Diffusion Models1 Jul
  12. 2021Score-based Generative Modeling in Latent Space10 Jun
5 more
  1. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  2. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  4. 2020Denoising Diffusion Implicit Models6 Oct
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 26

  1. 2017Attention Is All You Needcited by 59,932
  2. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  3. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  4. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  5. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  6. 2022Flow Matching for Generative Modelingcited by 5,426
  7. 2021Zero-Shot Text-to-Image Generationcited by 4,276
  8. 2018Large Scale GAN Training for High Fidelity Natural Image Synthesiscited by 2,609
  9. 2017Improved Training of Wasserstein GANscited by 2,223
  10. 2021Image Super-Resolution via Iterative Refinementcited by 1,506
  11. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  12. 2022Denoising Diffusion Restoration Modelscited by 951
14 more
  1. 2021Diffusion Probabilistic Models for 3D Point Cloud Generationcited by 734
  2. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  3. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 566
  4. 20213D Shape Generation and Completion through Point-Voxel Diffusioncited by 516
  5. 2021Grad-TTS: A Diffusion Probabilistic Model for Text-to-Speechcited by 445
  6. 2023Flow Matching on General Geometriescited by 260
  7. 2019Residual Flows for Invertible Generative Modelingcited by 256
  8. 2022Generative Modelling With Inverse Heat Dissipationcited by 164
  9. 2020VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Modelscited by 103
  10. 2021Understanding Failures in Out-of-Distribution Detection with Deep Generative Modelscited by 89
  11. 2018Bias and Generalization in Deep Generative Models: An Empirical Studycited by 83
  12. 2018Semi-Implicit Variational Inferencecited by 55
  13. 2022DiffGAN-TTS: High-Fidelity and Efficient Text-to-Speech with Denoising Diffusion GANscited by 43
  14. 2018Doubly Semi-Implicit Variational Inferencecited by 19

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 4; 2025: 4; 2026: 2.

13 papers.

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By area:

  1. 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 43
  2. 2023Label-Retrieval-Augmented Diffusion Models for Learning from Noisy Labelscited by 20
  3. 2023Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modelingcited by 17
  4. 2023DiracDiffusion: Denoising and Incremental Reconstruction with Assured Data-Consistencycited by 14
  5. 2024Stiefel Flow Matching for Moment-Constrained Structure Elucidationcited by 5
  6. 2025Guided Star-Shaped Masked Diffusioncited by 5
  7. 2024G2D2: Gradient-Guided Discrete Diffusion for Inverse Problem Solvingcited by 4
  8. 2025MiAD: Mirage Atom Diffusion for De Novo Crystal Generationcited by 3
  9. 2024SDP: Spiking Diffusion Policy for Robotic Manipulation with Learnable Channel-Wise Membrane Thresholdscited by 1
  10. 2025On Designing Diffusion Autoencoders for Efficient Generation and Representation Learningcited by 1
  11. 2026Perspectives on Tsallis Statistics for Artificial Intelligencecited by 1
  12. 2025Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equationscited by 0
1 more
  1. 2026γ-Bridge: A Look-Parametric Diffusion Bridgecited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Denoising Diffusion Probabilistic Models in Six Simple Steps
  2. 2023SPD-DDPM: Denoising Diffusion Probabilistic Models in the Symmetric Positive Definite Space
  3. 2025Assessing the Quality of Denoising Diffusion Models in Wasserstein Distance: Noisy Score and Optimal Bounds
  4. 2024Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality
  5. 2024Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models
  6. 2024O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
  7. 2023Improving Denoising Diffusion Probabilistic Models via Exploiting Shared Representations
  8. 2025Diffusion Models: A Mathematical Introduction