diffusions, sampling, and transport

The third and final day of the workshop was shortened for me as I had to catch an early flight back to Paris (and as I got overly conservative in my estimation for returning to JFK, catching a train with no delay at Penn Station and thus finding myself with two hours free before boarding, hence reviewing remaining Biometrika submission at the airport while waiting). As a result I missed the afternoon talks.

The morning was mostly about using scores for simulation (a topic of which I was mostly unaware), with Yang Song giving the introductory lecture on creating better [cf pix left] generative models via the score function, with a massive production of his on the topic (but too many image simulations of dogs, cats, and celebrities!). Estimating directly the score is feasible via Fisher divergence or score matching à la Hyvärinen (with a return of Stein’s unbiased estimator of the risk!). And relying on estimated scores to simulate / generate by Langevin dynamics or other MCMC methods that do not require density evaluations. Due to poor performances in low density / learning regions a fix is randomization / tempering but the resolution (as exposed) sounded clumsy. (And made me wonder at using some more advanced form of deconvolution since the randomization pattern is controlled.) The talk showed some impressive text to image simulations used by an animation studio!

And then my friend Arnaud Doucet continued on the same theme, motivating by estimating normalising constant through annealed importance sampling [Yuling’s meta-perspective comes back to mind in that the geometric mixture is not the only choice, but with which objective]. In AIS, as in a series of Arnaud’s works, like the 2006 SMC Read Paper with Pierre Del Moral and Ajay Jasra, the importance (!) of some auxiliary backward kernels goes beyond theoretical arguments, with the ideally sequence being provided by a Langevin diffusion. Hence involving a score, learned as in the previous talk. Arnaud reformulated this issue as creating a transportation map and its reverse, which is leading to their recent Schrödinger bridge generative model. Which [imho] both brings a unification perspective to his work and an efficient way to bridge prior to posterior in AIS. A most profitable morn for me!

Overall, this was an exhilarating workshop, full of discoveries for me and providing me with the opportunity to meet and exchange with mostly people I had not met before. Thanks to Bob Carpenter and Michael Albergo for organising and running the workshop!