Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
126 tokens/sec
GPT-4o
47 tokens/sec
Gemini 2.5 Pro Pro
43 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
47 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Stochastic interpolants with data-dependent couplings (2310.03725v3)

Published 5 Oct 2023 in cs.LG and stat.ML

Abstract: Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through samples, while the other is taken as a simple base density that is data-agnostic. In this work, using the framework of stochastic interpolants, we formalize how to \textit{couple} the base and the target densities, whereby samples from the base are computed conditionally given samples from the target in a way that is different from (but does preclude) incorporating information about class labels or continuous embeddings. This enables us to construct dynamical transport maps that serve as conditional generative models. We show that these transport maps can be learned by solving a simple square loss regression problem analogous to the standard independent setting. We demonstrate the usefulness of constructing dependent couplings in practice through experiments in super-resolution and in-painting.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (49)
  1. Building normalizing flows with stochastic interpolants. arXiv preprint arXiv:2209.15571, 2022.
  2. Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797, 2023.
  3. Cold diffusion: Inverting arbitrary image transforms without noise. arXiv preprint arXiv:2208.09392, 2022.
  4. Ricky T. Q. Chen. torchdiffeq, 2018. URL https://github.com/rtqichen/torchdiffeq.
  5. Riemannian flow matching on general geometries. arXiv preprint arXiv:2302.03660, 2023.
  6. Marco Cuturi. Sinkhorn distances: Lightspeed computation of optimal transport. Advances in neural information processing systems, 26, 2013.
  7. Flow matching in latent space. arXiv preprint arXiv:2307.08698, 2023.
  8. Soft diffusion: Score matching for general corruptions. arXiv preprint arXiv:2209.05442, 2022.
  9. Diffusion schrödinger bridge with applications to score-based generative modeling. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, volume 34, pp.  17695–17709. Curran Associates, Inc., 2021. URL https://proceedings.neurips.cc/paper_files/paper/2021/file/940392f5f32a7ade1cc201767cf83e31-Paper.pdf.
  10. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34:8780–8794, 2021.
  11. Density Estimation Using Real NVP. In International Conference on Learning Representations, pp.  32, 2017.
  12. Neural spline flows. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett (eds.), Advances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. URL https://proceedings.neurips.cc/paper/2019/file/7ac71d433f282034e088473244df8c02-Paper.pdf.
  13. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12598, 2022.
  14. Denoising diffusion probabilistic models. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin (eds.), Advances in Neural Information Processing Systems, volume 33, pp.  6840–6851. Curran Associates, Inc., 2020a. URL https://proceedings.neurips.cc/paper/2020/file/4c5bcfec8584af0d967f1ab10179ca4b-Paper.pdf.
  15. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840–6851, 2020b.
  16. Cascaded diffusion models for high fidelity image generation. The Journal of Machine Learning Research, 23(1):2249–2281, 2022a.
  17. Video diffusion models. arXiv:2204.03458, 2022b.
  18. Latent space editing in transformer-based flow matching. In ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems, 2023.
  19. Deep Networks with Stochastic Depth. arXiv:1603.09382 [cs], July 2016.
  20. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
  21. Auto-Encoding Variational Bayes. arXiv [Preprint], 0, 2013. URL https://arxiv.org/1312.6114v10.
  22. Equivariant flow matching, 2023.
  23. Minimizing trajectory curvature of ode-based generative models. arXiv preprint arXiv:2301.12003, 2023.
  24. Flow matching for generative modeling, 2022a. URL https://arxiv.org/abs/2210.02747.
  25. Flow matching for generative modeling. arXiv preprint arXiv:2210.02747, 2022b.
  26. I2superscriptI2\text{I}^{2}I start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPTsb: Image-to-image schr\\\backslash\” odinger bridge. arXiv preprint arXiv:2302.05872, 2023a.
  27. Qiang Liu. Rectified flow: A marginal preserving approach to optimal transport, 2022. URL https://arxiv.org/abs/2209.14577.
  28. Flow straight and fast: Learning to generate and transfer data with rectified flow, 2022a. URL https://arxiv.org/abs/2209.03003.
  29. Flow straight and fast: Learning to generate and transfer data with rectified flow. arXiv preprint arXiv:2209.03003, 2022b.
  30. Instaflow: One step is enough for high-quality diffusion-based text-to-image generation. arXiv preprint arXiv:2309.06380, 2023b.
  31. Improved denoising diffusion probabilistic models. In International Conference on Machine Learning, pp. 8162–8171. PMLR, 2021.
  32. Multisample flow matching: Straightening flows with minibatch couplings. arXiv preprint arXiv:2304.14772, 2023.
  33. Variational Inference with Normalizing Flows. In International Conference on Machine Learning, pp. 1530–1538. PMLR, June 2015.
  34. Image super-resolution via iterative refinement. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(4):4713–4726, 2022.
  35. Structure-based drug design with equivariant diffusion models. arXiv preprint arXiv:2210.13695, 2022.
  36. Conditional simulation using diffusion schrödinger bridges. In The 38th Conference on Uncertainty in Artificial Intelligence, 2022. URL https://openreview.net/forum?id=H9Lu6P8sqec.
  37. Diffusion schrödinger bridge matching, 2023.
  38. Where to diffuse, how to diffuse, and how to get back: Automated learning for multivariate diffusions. In The Eleventh International Conference on Learning Representations, 2023.
  39. Deep unsupervised learning using nonequilibrium thermodynamics. In International conference on machine learning, pp. 2256–2265. PMLR, 2015.
  40. Aligned diffusion schrödinger bridges. In The 39th Conference on Uncertainty in Artificial Intelligence, 2023. URL https://openreview.net/forum?id=BkWFJN7_bQ.
  41. Improved techniques for training score-based generative models. Advances in neural information processing systems, 33:12438–12448, 2020.
  42. Score-based generative modeling through stochastic differential equations. arXiv preprint arXiv:2011.13456, 2020.
  43. Maximum likelihood training of score-based diffusion models. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P.S. Liang, and J. Wortman Vaughan (eds.), Advances in Neural Information Processing Systems, volume 34, pp.  1415–1428. Curran Associates, Inc., 2021a. URL https://proceedings.neurips.cc/paper/2021/file/0a9fdbb17feb6ccb7ec405cfb85222c4-Paper.pdf.
  44. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021b.
  45. A family of nonparametric density estimation algorithms. Communications on Pure and Applied Mathematics, 66(2):145–164, 2013. doi: https://doi.org/10.1002/cpa.21423. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.21423.
  46. Density estimation by dual ascent of the log-likelihood. Communications in Mathematical Sciences, 8(1):217–233, 2010. ISSN 15396746, 19450796. doi: 10.4310/CMS.2010.v8.n1.a11.
  47. Improving and generalizing flow-based generative models with minibatch optimal transport. In ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems, 2023.
  48. Diffusion probabilistic modeling of protein backbones in 3d for the motif-scaffolding problem. arXiv preprint arXiv:2206.04119, 2022.
  49. Practical and asymptotically exact conditional sampling in diffusion models. arXiv preprint arXiv:2306.17775, 2023.
Citations (19)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now