Optimal Transport (OT) is one of those mathematical frameworks that quietly powers a surprising amount of modern machine learning, and yet remains underappreciated outside a small circle of researchers. This resource, hosted by Gabriel Peyré — coauthor of the seminal Computational Optimal Transport book and a driving force behind the field's practical accessibility — appears to be a dedicated course or reference site aimed at ML practitioners rather than pure mathematicians.

Why does this matter? OT gives you a principled way to measure distances between probability distributions by asking: what's the cheapest way to move one pile of mass into the shape of another? That deceptively simple question underlies an enormous amount of contemporary work:

• Generative models — Wasserstein GANs, flow matching, and diffusion model theory all lean on OT distances instead of KL divergence, sidestepping mode collapse and vanishing gradients.
• Domain adaptation — transporting a source distribution onto a target distribution is a natural way to align feature spaces across datasets.
• Single-cell genomics and trajectory inference — OT reconstructs cell-state transitions from static snapshots, one of the hottest applications in computational biology.
• Point cloud registration, NLP embeddings alignment, fairness-constrained classification — the applications keep multiplying.

The historical barrier has been computational: exact OT scales as O(n³ log n), which killed practical use for decades. The breakthrough was Sinkhorn divergences — entropic regularization that turns OT into a GPU-friendly matrix-scaling problem solvable in near-linear time. Peyré and Marco Cuturi's work made this accessible via the POT and OTT-JAX libraries, which is likely what this site teaches you to use.

For a technical audience, materials like this are gold because OT sits at an awkward intersection: the mathematical literature is dense with measure theory and convex duality, while blog posts tend to hand-wave the actual algorithms. A dedicated ML-focused treatment from someone who genuinely understands both sides is rare.

If you've ever wondered why your GAN training was unstable, why KL divergence feels wrong for comparing empirical distributions, or how diffusion models really connect to stochastic differential equations, OT is the underlying language. This resource likely offers the shortest path from "I've heard of Wasserstein distance" to actually deploying it in a research pipeline.