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Modern generative models exhibit unprecedented capabilities to generateextremely realistic data. However, given the inherent compositionality of thereal world, reliable use of these models in practical applications requiresthat they exhibit the capability to compose a novel set of concepts to generateoutputs not seen in the training data set. Prior work demonstrates that recentdiffusion models do exhibit intriguing compositional generalization abilities,but also fail unpredictably. Motivated by this, we perform a controlled studyfor understanding compositional generalization in conditional diffusion modelsin a synthetic setting, varying different attributes of the training data andmeasuring the model's ability to generate samples out-of-distribution. Ourresults show: (i) the order in which the ability to generate samples from aconcept and compose them emerges is governed by the structure of the underlyingdata-generating process; (ii) performance on compositional tasks exhibits asudden "emergence" due to multiplicative reliance on the performance ofconstituent tasks, partially explaining emergent phenomena seen in generativemodels; and (iii) composing concepts with lower frequency in the training datato generate out-of-distribution samples requires considerably more optimizationsteps compared to generating in-distribution samples. Overall, our study lays afoundation for understanding capabilities and compositionality in generativemodels from a data-centric perspective.

Compositional Abilities Emerge Multiplicatively: Exploring Diffusion Models on a Synthetic Task