# Thermodynamic Diffusion Inference with Minimal Digital Conditioning

arXiv: https://arxiv.org/abs/2604.14332 · HTML: https://mlsanity.com/paper/2604.14332/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 9 of its 14 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 9 of 9)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [An efficient probabilistic hardware architecture for diffusion-like models](https://mlsanity.com/paper/2510.23972/) (2025)

## Built on by (most cited first, 1 of 1)

- [Symmetric Equilibrium Propagation for Thermodynamic Diffusion Training](https://mlsanity.com/paper/2604.23806/) (2026)

## Abstract (arXiv)

Diffusion-model inference and overdamped Langevin dynamics are formally identical. A physical substrate that encodes the score function therefore equilibrates to the correct output by thermodynamics alone, requiring no digital arithmetic during inference and potentially achieving a 10,000× reduction in energy relative to a GPU. Two fundamental barriers have until now prevented this equivalence from being realized at production scale: non-local skip connections, which locally coupled analog substrates cannot represent, and input conditioning, in which the coupling constants carry roughly 2,600× too little signal to anchor the system to a specific input. We resolve both obstacles. Hierarchical bilinear coupling encodes U-Net skip connections as rank-k inter-module interactions derived directly from the singular structure of the encoder and decoder Gram matrices, requiring only O(Dk) physical connections instead of O(D2). A minimal digital interface -- a 4-dimensional bottleneck encoder together with a 16-unit transfer network, totalling 2,560 parameters -- overcomes the conditioning barrier. When evaluated on activations drawn from a trained denoising U-Net, the complete system attains a decoder cosine similarity of 0.9906 against an oracle upper bound of 1.0000, while preserving theoretical net energy savings of approximately 107× over GPU inference. These results constitute the first demonstration of trained-weight, production-scale thermodynamic diffusion inference.