Beyond the Black Box: Identifiable Interpretation and Control in Generative Models via Causal Minimality

TL;DR

This paper establishes a causal minimality framework for interpretable generative models, enabling clear causal understanding and control of latent representations, with empirical validation on text-to-image diffusion models.

Contribution

It introduces a theoretical foundation for hierarchical, interpretable generative models based on causal minimality, and demonstrates practical extraction and control of concepts in diffusion models.

Findings

Latent representations can be aligned with true data-generating variables.

Hierarchical concept graphs can be extracted from diffusion models.

Causal constraints enable fine-grained model steering.

Abstract

Deep generative models, while revolutionizing fields like image and text generation, largely operate as opaque ``black boxes'', hindering human understanding, control, and alignment. While methods like sparse autoencoders (SAEs) show remarkable empirical success, they often lack theoretical guarantees, risking subjective insights. Our primary objective is to establish a principled foundation for interpretable generative models. We demonstrate that the principle of causal minimality -- favoring the simplest causal explanation -- can endow the latent representations of modern generative models with clear causal interpretation and robust, component-wise identifiable control. We introduce a novel theoretical framework for hierarchical selection models, where higher-level concepts emerge from the constrained composition of lower-level variables, better capturing the complex dependencies in data generation. Under theoretically derived minimality conditions, we show that learned representations can be equivalent to the true latent variables of the data-generating process. Empirically, applying these constraints to leading text-to-image diffusion models allows us to extract their innate hierarchical concept graphs, offering fresh insights into their internal knowledge organization. Furthermore, these causally grounded concepts serve as levers for fine-grained model steering, paving the way for transparent, reliable systems.