# Scalable Discrete-to-Continuous Channel Simulation for Compression and Privacy

arXiv: https://arxiv.org/abs/2609.12067 · HTML: https://mlsanity.com/paper/2609.12067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 57 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 25 of 25)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Language Model Beats Diffusion -- Tokenizer is Key to Visual Generation](https://mlsanity.com/paper/2310.05737/) (2023)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Lossy Compression with Gaussian Diffusion](https://mlsanity.com/paper/2206.08889/) (2022)
- [SQ-VAE: Variational Bayes on Discrete Representation with Self-annealed Stochastic Quantization](https://mlsanity.com/paper/2205.07547/) (2022)
- [Minimal Random Code Learning: Getting Bits Back from Compressed Model Parameters](https://mlsanity.com/paper/1810.00440/) (2018)
- [Compressing Images by Encoding Their Latent Representations with Relative Entropy Coding](https://mlsanity.com/paper/2010.01185/) (2020)
- [Algorithms for the Communication of Samples](https://mlsanity.com/paper/2110.12805/) (2021)
- [Lossless Compression of Efficient Private Local Randomizers](https://mlsanity.com/paper/2102.12099/) (2021)
- [Lossy Compression with Pretrained Diffusion Models](https://mlsanity.com/paper/2501.09815/) (2025)
- [Optimal Compression of Locally Differentially Private Mechanisms](https://mlsanity.com/paper/2111.00092/) (2021)
- [Privacy Amplification via Compression: Achieving the Optimal Privacy-Accuracy-Communication Trade-off in Distributed Mean Estimation](https://mlsanity.com/paper/2304.01541/) (2023)
- [Compression with Exact Error Distribution for Federated Learning](https://mlsanity.com/paper/2310.20682/) (2023)
- [Communication-Efficient Laplace Mechanism for Differential Privacy via Random Quantization](https://mlsanity.com/paper/2309.06982/) (2023)
- [Communication Efficient Private Federated Learning Using Dithering](https://mlsanity.com/paper/2309.07809/) (2023)
- [Universal Exact Compression of Differentially Private Mechanisms](https://mlsanity.com/paper/2405.20782/) (2024)
- [Communication-Efficient and Privacy-Adaptable Mechanism for Federated Learning](https://mlsanity.com/paper/2501.12046/) (2025)
- [Channel Simulation and Distributed Compression with Ensemble Rejection Sampling](https://mlsanity.com/paper/2510.05552/) (2025)
- [Training-Free Vector Quantization via Gaussian VAEs](https://mlsanity.com/paper/2512.06609/) (2025)
- [SoftBinary Coding: A New Information-Theoretic Neural Compression Paradigm](https://mlsanity.com/paper/2606.29578/) (2026)

## Abstract (arXiv)

Channel simulation has recently emerged as a useful component in machine learning systems where samples from a prescribed probability distribution are to be compressed. Yet, general channel simulation algorithms often suffer from high computational costs, random stopping times or, in the worst case, can require generating an infinite number of shared random samples. We introduce a scheme for both exact and approximate simulation of discrete-to-continuous channels which conversely uses a fixed number of random samples, and therefore has a runtime independent of the channel and the input. Unlike existing channel simulation schemes which generate a sequence of independent samples from a proposal distribution, our approach generates one sample, or alternatively a fixed number of samples, from each potential target distribution. We then apply a latent permutation to the samples before performing sample selection using an exponential race. Our scheme provides a flexible tradeoff between the number of generated samples and the compression rate. Using polar and multilevel coding, we scale our approach to handle long blocklengths in O(n log n) time in order to benefit from reduced per-symbol overhead. We conclude by demonstrating applications to variable-rate compression with stochastic VQ-VAEs and communication-efficient differentially private distributed mean estimation via exact simulation of the Gaussian mechanism.