# A Generative Sampler for distributions with possible discrete parameter based on Reversibility

arXiv: https://arxiv.org/abs/2603.09251 · HTML: https://mlsanity.com/paper/2603.09251/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 10 Mar 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Integer Discrete Flows and Lossless Compression](https://mlsanity.com/paper/1905.07376/) (2019)
- [Smooth Normalizing Flows](https://mlsanity.com/paper/2110.00351/) (2021)
- [Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions](https://mlsanity.com/paper/1604.05251/) (2016)
- [Metrizing Weak Convergence with Maximum Mean Discrepancies](https://mlsanity.com/paper/2006.09268/) (2020)
- [A consensus-based global optimization method for high dimensional machine learning problems](https://mlsanity.com/paper/1909.09249/) (2019)
- [A consensus-based model for global optimization and its mean-field limit](https://mlsanity.com/paper/1604.05648/) (2016)
- [Learning Discrete Distributions by Dequantization](https://mlsanity.com/paper/2001.11235/) (2020)
- [Optimal Variance Control of the Score Function Gradient Estimator for Importance Weighted Bounds](https://mlsanity.com/paper/2008.01998/) (2020)
- [Weak Generative Sampler to Efficiently Sample Invariant Distribution of Stochastic Differential Equation](https://mlsanity.com/paper/2405.19256/) (2024)

## Abstract (arXiv)

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to discrete or mixed-variable systems remains difficult due to ill-defined gradients or high variance in estimators. We propose a unified, target-gradient-free generative sampling framework applicable across diverse state spaces. Building on the fact that detailed balance implies the time-reversibility of the equilibrium stochastic process, we enforce this symmetry as a statistical constraint. Specifically, using a prescribed physical transition kernel (such as Metropolis-Hastings), we minimize the Maximum Mean Discrepancy (MMD) between the joint distributions of forward and backward Markov trajectories. Crucially, this training procedure relies solely on energy evaluations via acceptance ratios, circumventing the need for target score functions or continuous relaxations. We demonstrate the versatility of our method on three distinct benchmarks: (1) a continuous multi-modal Gaussian mixture, (2) the discrete high-dimensional Ising model, and (3) a challenging hybrid system coupling discrete indices with continuous dynamics. Experiments show that our framework accurately reproduces thermodynamic observables and captures mode-switching behavior across all regimes, offering a physically grounded and universally applicable alternative for equilibrium sampling.