The Schrödinger bridge finds the most likely diffusion path between two distributions — entropy-regularized optimal transport. Particles travel from source μ₀ to target μ₁ via optimal stochastic trajectories, minimizing KL divergence from Brownian motion.
60
0.08
Time t/T
0.00
KL cost (est)
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W₂ cost (est)
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Schrödinger Bridge: min_{P∈Π(μ₀,μ₁)} KL(P‖W) where W is Wiener measure.
Solution: dXₜ = [∇ log φₜ(Xₜ)] dt + σ dBₜ — Doob h-transform of Brownian motion between marginals.