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Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate

arXiv:2606.23920v1 Announce Type: cross Abstract: The task of compositional generation involves using a conditional generative model, trained only on a subset of the possible conditions, to produce samples from compositionally-defined target distributions such as a geometric combination of the source distributions. In this work, we argue that this task is often infeasible for vanilla conditional diffusion models: we conjecture that no inference-time technique can efficiently produce samples from the target distribution in certain well-motivated settings. This idea is supported by theory-guided generalization arguments and carefully-designed experiments on both synthetic and realistic data. In particular, while recent methods such as Feynman-Kac correction reduce inference-time approximation error, our results show that score estimation error has a more catastrophic effect on performance when the target distribution is out-of-distribution with respect to the sources, highlighting the need for a different approach to this task.

Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation

arXiv:2606.18509v1 Announce Type: new Abstract: Reliable generalization in conditional latent variable models requires understanding both identifiability and extrapolation: how observed variation across attributes determines latent structure, and how that structure determines distributions at unseen attributes. However, existing identifiability and extrapolation guarantees are largely model-specific, with separate analyses in nonlinear ICA, causal representation learning, perturbation modeling, and related conditional latent variable models. We introduce concept modulation models (CMMs), an attribute-indexed class of conditional generative models with structure $A\to \Lambda \to C\to X$, where attributes select modulators, modulators induce latent concept laws, and concepts generate observed features. CMMs lift transition-based identifiability to conditional settings by showing that feature agreement on observed attributes induces a latent concept transition constrained by the CMM class. We express these constraints through attribute potentials, log-density ratios between attribute-conditioned concept laws, separating the generic lifting step from model-specific rigidity arguments. The same potentials control extrapolation: agreement at unseen attributes holds exactly when the transported attribute-potential identities extend to those attributes. This yields algebraic extrapolation criteria, identifies the common potential-based proof objects behind several existing identifiability and extrapolation results, and, when combined with the model-specific rigidity arguments in those works, recovers their stated conclusions.