Finally, something that is not obvious at all, and requires some digging / equation re-writing. SD3's (arxiv.org/abs/2403.03206) Flow matching weighting is very similar to EDM's weighting (arxiv.org/abs/2206.00364).
Above FM does not actually look that straight, an often claimed feature of FM. What's going on?
- FM schedule (often omitted "OT") is straight to a single point (possibly with tiny noise). - Unfortunately, that does not guarantee straightness between distributions.
DDIM vs Flow Matching. Note whatever schedule (alpha/sigma, VP, VE, FM) we pick, DDIM always ends up at the same spot: - DDIM is invariant to alpha/sigma rescalings - With FM schedule, sampling with either DDIM and Euler (=what FM uses) is the same.
This is a really nice blogpost by @RuiqiGao and team that I enjoyed being a part of. My favorite key learnings are: - DDIM sampler == flow matching sampling - (Not) straight? - SD3 weighting (Esser, Rombach, et al) is very similar to the EDM weighting (Karras, et al). 👇
A common question nowadays: Which is better, diffusion or flow matching? 🤔
Our answer: They’re two sides of the same coin. We wrote a blog post to show how diffusion models and Gaussian flow matching are equivalent. That’s great: It means you can use them interchangeably.
