# Complementary Characterization of Agent-Based Models via Computational Mechanics and Diffusion Models

arXiv: https://arxiv.org/abs/2512.04771 · HTML: https://mlsanity.com/paper/2512.04771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Placed in

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

## Builds on (most cited first, 7 of 7)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Characterizing Agent-Based Model Dynamics via ε-Machines and Kolmogorov-Style Complexity](https://mlsanity.com/paper/2510.12729/) (2025)

## Abstract (arXiv)

This article extends the preprint "Characterizing Agent-Based Model Dynamics via ε-Machines and Kolmogorov-Style Complexity" by introducing diffusion models as orthogonal and complementary tools for characterizing the output of agent-based models (ABMs). Where ε-machines capture the predictive temporal structure and intrinsic computation of ABM-generated time series, diffusion models characterize high-dimensional cross-sectional distributions, learn underlying data manifolds, and enable synthetic generation of plausible population-level outcomes. We provide a formal analysis demonstrating that the two approaches operate on distinct mathematical domains -- processes vs. distributions -- and show that their combination yields a two-axis representation of ABM behavior based on temporal organization and distributional geometry. To our knowledge, this is the first framework to integrate computational mechanics with score-based generative modeling for the structural analysis of ABM outputs, thereby situating ABM characterization within the broader landscape of modern machine-learning methods for density estimation and intrinsic computation. The framework is validated using the same elder-caregiver ABM dataset introduced in the companion paper, and we provide precise definitions and propositions formalizing the mathematical complementarity between ε-machines and diffusion models. This establishes a principled methodology for jointly analyzing temporal predictability and high-dimensional distributional structure in complex simulation models.