Standard training methods currently avoid computing the Jacobian explicitly.
Highly under-appreciated fact: Jacobian of your denoiser is the most mathematically consequential part of a diffusion model. Architecture gets all the attention, but the Jacobian governs everything - even if standard training methods mean you never actually have to look at it
Users affirm that the Jacobian of the denoiser governs diffusion model mathematics because its impact is often overlooked.
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@docmilanfar What are some capabilities enabled by working with the Jacobian?
@docmilanfar Yep, essentially all of my diffusion papers are about looking at the Jacobian from this or that angle
@docmilanfar Architecture attracts attention. Decision-making determines outcomes.
@docmilanfar My understanding is that The Jacobian tells you how the geometry of the entire distribution evolves but this is usually hidden beneath the score
@docmilanfar totally agree, the jacobian's impact is often overlooked.
@docmilanfar Would love to see Jacobian spectra compared across denoiser architectures. Probably more revealing than another ablation study.