# Generative Models on Analog Hardware with Dynamics

arXiv: https://arxiv.org/abs/2606.27294 · HTML: https://mlsanity.com/paper/2606.27294/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Training Deep Boltzmann Networks with Sparse Ising Machines](https://mlsanity.com/paper/2303.10728/) (2023)
- [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025)
- [Optical Diffusion Models for Image Generation](https://mlsanity.com/paper/2407.10897/) (2024)
- [Neural Langevin Machine: a local asymmetric learning rule can be creative](https://mlsanity.com/paper/2506.23546/) (2025)
- [Stuart-Landau Oscillatory Graph Neural Network](https://mlsanity.com/paper/2511.08094/) (2025)
- [OscNet v1.5: Energy Efficient Hopfield Network on CMOS Oscillators for Image Classification](https://mlsanity.com/paper/2506.12610/) (2025)

## Built on by (most cited first, 2 of 2)

- [Analog-Friendly Predictive Coding without Activation Derivatives](https://mlsanity.com/paper/2609.32350/) (2026)
- [Physical Muon: Orthogonalization as an Equilibrium Computation](https://mlsanity.com/paper/2609.37525/) (2026)

## Abstract (arXiv)

Analog hardware platforms such as coupled oscillators and Analog Ising Machines naturally solve differential equations at a fraction of the energy cost of digital computation, making them attractive for low-power generative modeling, yet a fundamental mismatch exists: modern generative models assume flexible, software-defined dynamics, whereas analog hardware imposes fixed, physics-determined differential equations with limited approximation capacity. This paper introduces Analog Interaction Systems (AIS), a unified framework for hardware-implementable dynamical systems, and empirically characterizes their expressivity gap relative to neural network baselines. Two hardware-compatible mechanisms are proposed to narrow this gap - time-varying piecewise parameters and hidden physical states - and a Wasserstein GAN training procedure is developed to enable training of these models without requiring them to follow a specific trajectory. We characterize how area and power scale with connection density and precision, showing that sparse connectivity and low-bit-width quantized parameters are necessary for practical implementation, and estimate an energy cost of 23uJ per generated image for the chosen architecture, representing a 2-orders-of-magnitude improvement over digital baselines. On MNIST and Fashion-MNIST, our oscillator-based AIS achieves FID scores of 27.6 and 80.8, outperforming the best prior hardware-implementable analog generative models by 3-4x with a 4-bit sparse architecture.