Our main results study when projective composition is achieved by linearly combining scores.
We prove it suffices for particular independence properties to hold in pixel-space. Importantly, some results extend to independence in feature-space... but new complexities also arise (see the paper!) 5/5

We formalize this idea with a definition called Projective Composition — based on projection functions that extract the “key features” for each distribution to be composed. 4/

What does it mean for composition to "work" in these diverse settings? We need to specify which aspects of each distribution we care about— i.e. the “key features” that characterize a hat, dog, horse, or object-at-a-location. The "correct" composition should have all the features at once. 3/

Part of challenge is, we may want compositions to be OOD w.r.t. the distributions being composed. For example in this CLEVR experiment, we trained diffusion models on images of a *single* object conditioned on location, and composed them to generate images of *multiple* objects. 2/

Credit to: x.com/sjforman/sta...

Happy for you Peli!!

for example I never trust an experiment in a paper unless (a) I know the authors well or (b) I’ve reproduced the results myself

imo most academics are skeptical of papers? It’s well-known that many accepted papers are overclaimed or just wrong— there’s only a few papers people really pay attention to despite the volume

This optimal denoiser has a closed-form for finite train sets, and notably does not reproduce its train set; it can sort of "compose consistent patches." Good exercise for reader: work out the details to explain Figure 3.

Neat, I’ll take a closer look! (I think I saw an earlier talk you gave on this as well)