Valentin De Bortoli
@vdebortoli.bsky.social
messing up with gaussians
I love a good illustration 😍
December 15, 2024 at 12:40 AM
I love a good illustration 😍
Don't miss it!
December 14, 2024 at 4:40 AM
Don't miss it!
yeah we tried to make it more accessible in arxiv.org/abs/2303.16852 and arxiv.org/abs/2409.09347 but we should definitely work on an easier intro, cc. @jamesthornton.bsky.social 👀
Diffusion Schrödinger Bridge Matching
Solving transport problems, i.e. finding a map transporting one given distribution to another, has numerous applications in machine learning. Novel mass transport methods motivated by generative model...
arxiv.org
December 13, 2024 at 9:07 PM
yeah we tried to make it more accessible in arxiv.org/abs/2303.16852 and arxiv.org/abs/2409.09347 but we should definitely work on an easier intro, cc. @jamesthornton.bsky.social 👀
100% agree. OT is not (or rarely) a goal in itself but rather a mean to enforce useful properties
December 5, 2024 at 8:15 AM
100% agree. OT is not (or rarely) a goal in itself but rather a mean to enforce useful properties
Reposted by Valentin De Bortoli
Iterated RF with conservative vector fields should get to OT, though training remains a challenge
arxiv.org/abs/2209.14577
arxiv.org/abs/2209.14577
Rectified Flow: A Marginal Preserving Approach to Optimal Transport
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $π_0,π_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the ...
arxiv.org
December 4, 2024 at 7:02 AM
Iterated RF with conservative vector fields should get to OT, though training remains a challenge
arxiv.org/abs/2209.14577
arxiv.org/abs/2209.14577
ahah yeah apologies for this, I am slowly learning how to write for non-theoretical proba crowd but it's a process 😅
December 2, 2024 at 11:36 PM
ahah yeah apologies for this, I am slowly learning how to write for non-theoretical proba crowd but it's a process 😅
Yeah I was referring to the coupling obtained after the flow matching operation (or "Reflow"). It's an interesting object in itself which is not exactly OT but still exhibit *some* level of straightness.
December 2, 2024 at 11:29 PM
Yeah I was referring to the coupling obtained after the flow matching operation (or "Reflow"). It's an interesting object in itself which is not exactly OT but still exhibit *some* level of straightness.
I am a broken record but yeah totally agree. If you iterate FM on that coupling though you get OT though (If you add a bit of noise). In the case of noisy FM we showed that the only coupling that is left invariant by noisy FM is the EOT one in arxiv.org/abs/2311.06978
Augmented Bridge Matching
Flow and bridge matching are a novel class of processes which encompass diffusion models. One of the main aspect of their increased flexibility is that these models can interpolate between arbitrary d...
arxiv.org
December 2, 2024 at 7:22 PM
I am a broken record but yeah totally agree. If you iterate FM on that coupling though you get OT though (If you add a bit of noise). In the case of noisy FM we showed that the only coupling that is left invariant by noisy FM is the EOT one in arxiv.org/abs/2311.06978