# Electric Currents for Discrete Data Generation

arXiv: https://arxiv.org/abs/2509.23825 · HTML: https://mlsanity.com/paper/2509.23825/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 21 references that are in the map.
- First posted on arXiv 28 Sep 2025.

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications](https://mlsanity.com/paper/2402.03232/) (2024)
- [Field Matching: an Electrostatic Paradigm to Generate and Transfer Data](https://mlsanity.com/paper/2502.02367/) (2025)
- [Interaction Field Matching: Overcoming Limitations of Electrostatic Models](https://mlsanity.com/paper/2506.02950/) (2025)

## Abstract (arXiv)

We propose Electric Current Discrete Data Generation (ECD2G), a pioneering method for data generation in discrete settings that is grounded in electrical engineering theory. Our approach draws an analogy between electric current flow in a circuit and the transfer of probability mass between data distributions. We interpret samples from the source distribution as current input nodes of a circuit and samples from the target distribution as current output nodes. A neural network is then used to learn the electric currents to represent the probability flow in the circuit. To map the source distribution to the target, we sample from the source and transport these samples along the circuit pathways according to the learned currents. This process provably guarantees transfer between data distributions. We present proof-of-concept experiments to illustrate our ECD2G method.