We examine the theoretical foundations of composition in diffusion fashions, with a selected deal with out-of-distribution extrapolation and length-generalization. Prior work has proven that composing distributions through linear rating mixture can obtain promising outcomes, together with length-generalization in some circumstances (Du et al., 2023; Liu et al., 2022). Nevertheless, our theoretical understanding of how and why such compositions work stays incomplete. In actual fact, it’s not even totally clear what it means for composition to “work”. This paper begins to handle these elementary gaps. We start by exactly defining one attainable desired results of composition, which we name projective composition. Then, we examine: (1) when linear rating mixtures provably obtain projective composition, (2) whether or not reverse-diffusion sampling can generate the specified composition, and (3) the situations beneath which composition fails. Lastly, we join our theoretical evaluation to prior empirical observations the place composition has both labored or failed, for causes that had been unclear on the time.
