A Mechanistic Study of Algorithmic Generalization in Diffusion Models on Modular Arithmetic

Abstract:Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. In this work, we provide a controlled mechanistic account of algorithmic learning in diffusion models. By utilizing the grokking phenomenon on an image-based modular addition task as a tractable testbed, we dissect the model's internal dynamics across two distinct visual regimes. In a single-image regime, mechanistic dissection reveals that the model implements modular addition by encoding operands as periodic representations and composing them at the self-attention--feedforward interface in a way that recovers the trigonometric addition identities. In a diverse-image regime with high intraclass variability, we find that the iterative sampling process partitions the task into an arithmetic computation phase and a subsequent visual refinement phase, with their transition precisely captured by an internal frequency-entropy signal. Together, our analysis clarifies the mechanics of algorithmic generalization of diffusion models in a controlled setting, while leaving open how broadly these mechanisms transfer beyond modular addition.

Machine Learning (cs.LG)

arXiv:2604.17673 [cs.LG]

(or arXiv:2604.17673v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2604.17673 Focus to learn more arXiv-issued DOI via DataCite

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