mlsanityData to 14 Oct 2026

Integer Discrete Flows and Lossless Compression

arXiv 1905.07376 ↗First posted 17 May 2019cs.LG cs.CV stat.MLcited by 83

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Abstract (arXiv)

Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, conventional flows assume continuous data, which may lead to reconstruction errors when quantized for compression. For that reason, we introduce a flow-based generative model for ordinal discrete data called Integer Discrete Flow (IDF): a bijective integer map that can learn rich transformations on high-dimensional data. As building blocks for IDFs, we introduce a flexible transformation layer called integer discrete coupling. Our experiments show that IDFs are competitive with other flow-based generative models. Furthermore, we demonstrate that IDF based compression achieves state-of-the-art lossless compression rates on CIFAR10, ImageNet32, and ImageNet64. To the best of our knowledge, this is the first lossless compression method that uses invertible neural networks.

Key facts. Cited by 83 papers in the map (data through 14 Oct 2026). First posted on arXiv 17 May 2019.

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Citing papers per year: 2021: 27; 2022: 21; 2023: 8; 2024: 12; 2025: 7; 2026: 8.

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  1. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  2. 2021Argmax Flows and Multinomial Diffusion: Learning Categorical Distributionscited by 574
  3. 2022Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioningcited by 373
  4. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 252
  5. 2023Language Modeling Is Compressioncited by 225
  6. 2021Autoregressive Diffusion Modelscited by 210
  7. 2022An Introduction to Neural Data Compressioncited by 79
  8. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codescited by 71
  9. 2021Soft then Hard: Rethinking the Quantization in Neural Image Compressioncited by 51
  10. 2021Learning Partial Equivariances from Datacited by 45
  11. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  12. 2021Fair Normalizing Flowscited by 38
38 more
  1. 2021On the Out-of-distribution Generalization of Probabilistic Image Modellingcited by 33
  2. 2021iVPF: Numerical Invertible Volume Preserving Flow for Efficient Lossless Compressioncited by 27
  3. 2021iFlow: Numerically Invertible Flows for Efficient Lossless Compression via a Uniform Codercited by 26
  4. 2021Conditional Invertible Neural Networks for Diverse Image-to-Image Translationcited by 24
  5. 2022Deep Lossy Plus Residual Coding for Lossless and Near-lossless Image Compressioncited by 22
  6. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  7. 2021ANFIC: Image Compression Using Augmented Normalizing Flowscited by 20
  8. 2021Lossless Compression with Probabilistic Circuitscited by 20
  9. 2021Improving Lossless Compression Rates via Monte Carlo Bits-Back Codingcited by 19
  10. 2023Deep Generative Models for Detector Signature Simulation: A Taxonomic Reviewcited by 18
  11. 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
  12. 2021Learning Scalable ℓ_∞-constrained Near-lossless Image Compression via Joint Lossy Image and Residual Compressioncited by 16
  13. 2022Personalized Public Policy Analysis in Social Sciences using Causal-Graphical Normalizing Flowscited by 16
  14. 2021Towards Empirical Sandwich Bounds on the Rate-Distortion Functioncited by 14
  15. 2024Compression via Pre-trained Transformers: A Study on Byte-Level Multimodal Datacited by 13
  16. 2021LC-FDNet: Learned Lossless Image Compression with Frequency Decomposition Networkcited by 12
  17. 2022aiWave: Volumetric Image Compression with 3-D Trained Affine Wavelet-like Transformcited by 11
  18. 2022Semi-Discrete Normalizing Flows through Differentiable Tessellationcited by 11
  19. 2021Partition and Code: learning how to compress graphscited by 10
  20. 2024Generative Modeling of Discrete Joint Distributions by E-Geodesic Flow Matching on Assignment Manifoldscited by 9
  21. 2024Scaling Continuous Latent Variable Models as Probabilistic Integral Circuitscited by 9
  22. 2023Probabilistic Integral Circuitscited by 8
  23. 2023Approximating Human-Like Few-shot Learning with GPT-based Compressioncited by 7
  24. 2024Probabilistic Neural Circuitscited by 7
  25. 2024CALLIC: Content Adaptive Learning for Lossless Image Compressioncited by 6
  26. 2021Lossless Image Compression Using a Multi-Scale Progressive Statistical Modelcited by 5
  27. 2022Split Hierarchical Variational Compressioncited by 5
  28. 2022PILC: Practical Image Lossless Compression with an End-to-end GPU Oriented Neural Frameworkcited by 5
  29. 2022Few-Shot Non-Parametric Learning with Deep Latent Variable Modelcited by 5
  30. 2023Generative Marginalization Modelscited by 5
  31. 2024Understanding Likelihood of Normalizing Flow and Image Complexity through the Lens of Out-of-Distribution Detectioncited by 5
  32. 2024Learning Lossless Compression for High Bit-Depth Volumetric Medical Imagecited by 5
  33. 2021Lossless Compression with Latent Variable Modelscited by 4
  34. 2021Multi-Resolution Continuous Normalizing Flowscited by 4
  35. 2022Parallel Neural Local Lossless Compressioncited by 4
  36. 2022Practical Learned Lossless JPEG Recompression with Multi-Level Cross-Channel Entropy Model in the DCT Domaincited by 4
  37. 2022Fast Lossless Neural Compression with Integer-Only Discrete Flowscited by 4
  38. 2022Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Modelscited by 4

50 most cited of 83 All 83 (JSON)