Sinkhorn and the 1781 roots of AI's optimal transport

The explainer positions optimal transport as a unifying idea rather than a niche technique. It starts with Monge's 1781 question of moving soil at minimum effort, then shows how Kantorovich's 1942 relaxation allowed mass to be split, leading to the Wasserstein distance.

The turning point was Cuturi's 2013 introduction of entropic regularization and the Sinkhorn algorithm. That made the computation fast and differentiable, which the explainer says is why optimal transport moved into deep learning. From there, it connects the same math to diffusion models, domain adaptation, and even attention mechanisms, arguing that these are all variations on moving or comparing distributions.

The piece also maps out practical uses across biotech, finance, and logistics, noting for example that the moscot framework was published in Nature in 2025 and used optimal transport to align about 1.7 million mouse embryo cells across 20 time points. It concludes that the ability to compare or transform distributions is a transferable skill across these fields.