Diffusion Additive Models: Interpretable Generative Prediction through Feature-Wise Contributions

Generalized additive models (GAMs) for location, scale and shape yield non-linear, interpretable feature-wise effects. However, they require parametric assumptions about the conditional outcome distribution and represent feature effects through deterministic functions. We introduce Diffusion Additive Models (DAMs), a generative framework for interpretable probabilistic regression and classification. Rather than specifying the shape of the conditional outcome distribution directly, DAMs treat individual feature contributions as latent variables and model their full distributions. Learning these contributions is challenging because only their sum is observed. To make this underdetermined composition learnable, we construct an encoder from a closed-form approximate posterior and calibrate its feature-wise distributions using aggregated posterior moments and homoskedastic variance routing. We then use SDE Matching to distill these distributions into feature-specific latent stochastic differential equations. DAMs capture flexible, potentially multimodal feature contributions and propagate their uncertainty to the outcome, while retaining the additive interpretability of GAMs. Across diverse regression and classification benchmarks, DAM consistently matches or outperforms existing additive models in predictive accuracy and calibration.