On the Anisotropy of Score-Based Generative Models

Abstract:We investigate the role of network architecture in shaping the inductive biases of modern score-based generative models. To this end, we introduce the Score Anisotropy Directions (SADs), architecture-dependent directions that reveal how different networks preferentially capture data structure. Our analysis suggests that SADs form adaptive bases aligned with the architecture's output geometry, providing a principled way to predict generalization ability in score models prior to training. Through both synthetic data and standard image benchmarks, we demonstrate that SADs reliably capture fine-grained model behavior and correlate with downstream performance, as measured by Wasserstein metrics. Our work offers a new lens for explaining and predicting directional biases of generative models.

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2510.22899 [cs.LG]

(or arXiv:2510.22899v2 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2510.22899 Focus to learn more arXiv-issued DOI via DataCite

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