# Figure Notebooks This directory contains the executable notebooks that generate the illustrative figures currently included in the OT4ML book. Each live notebook writes one or several PDF panels to `../latex/figures//`; the thumbnails below are compact PNG previews rendered from those outputs. Rendered web version: [www.gpeyre.com/ot4ml/notebooks-figures/](https://www.gpeyre.com/ot4ml/notebooks-figures/). **Gallery status.** Checked against the current LaTeX and MyST sources: all 76 live `latex/figures//` directories referenced by `\includegraphics{figures/...}` have a matching live `.ipynb` file, thumbnail in [`thumbnails/`](thumbnails/), and generated PDF panels in `../latex/figures/`. The searchable gallery currently exposes 77 figure views, because `generative-diffusion-versus-ot-2d.ipynb` also provides the distinct schedule-comparison view. The book currently has 78 LaTeX figure labels because two figure directories generate two labeled figures each. The contact sheet below is built from the same active thumbnail set. This README intentionally lists only figure views integrated in the current LaTeX or MyST sources. Retired or exploratory notebooks live in [`removed/`](removed/), with their matching generated panels in [`../latex/figures/removed/`](../latex/figures/removed/). They are kept for provenance but omitted from this paper gallery. Open a notebook locally from the **Open notebook** link, or launch it in Google Colab from the badge. The Colab links target the `main` branch of [`gpeyre/ot4ml`](https://github.com/gpeyre/ot4ml). [![Contact sheet of book figures](thumbnails/book-figures-contact-sheet.png)](../README.md#figures-of-the-book) ## Optimal Matching between Point Clouds
One-dimensional quantile assignment
One-dimensional quantile assignment
Open notebook · Open in Colab 		Convex and concave costs on the line
Convex and concave costs on the line
Open notebook · Open in Colab 		Histogram equalization as one-dimensional Monge transport
Histogram equalization as one-dimensional Monge transport
Open notebook · Open in Colab
Circle transport by cutting and unfolding
Circle transport by cutting and unfolding
Open notebook · Open in Colab 		Two-dimensional assignments for different cost exponents
Two-dimensional assignments for different cost exponents
Open notebook · Open in Colab 		Resolution and nonuniform weights in discrete transport
Resolution and nonuniform weights in discrete transport
Open notebook · Open in Colab
Rational weights as duplicated matchings
Rational weights as duplicated matchings
Open notebook · Open in Colab 		Hungarian algorithm progression
Hungarian algorithm progression
Open notebook · Open in Colab
## Monge Problem between Measures
RGB color transfer by a Monge map
RGB color transfer by a Monge map
Open notebook · Open in Colab 		McCann interpolation between two shapes
McCann interpolation between two shapes
Open notebook · Open in Colab 		One-dimensional quantiles and displacement interpolation
One-dimensional quantiles and displacement interpolation
Open notebook · Open in Colab
Triangular rearrangement between two silhouettes
Triangular rearrangement between two silhouettes
Open notebook · Open in Colab 		Gaussian W2 geodesics and Bures ellipses
Gaussian W2 geodesics and Bures ellipses
Open notebook · Open in Colab
## Kantorovich Relaxation
Couplings as straight transport segments
Couplings as straight transport segments
Open notebook · Open in Colab 		Coupling matrices with marginals
Coupling matrices with marginals
Open notebook · Open in Colab 		From permutation matrices to splitting couplings
From permutation matrices to splitting couplings
Open notebook · Open in Colab
Logarithmic barrier central path
Logarithmic barrier central path
Open notebook · Open in Colab 		McCann interpolation from a transport plan
McCann interpolation from a transport plan
Open notebook · Open in Colab 		Discrete gluing lemma
Discrete gluing lemma
Open notebook · Open in Colab
Quantitative central-limit theorem
Quantitative central-limit theorem
Open notebook · Open in Colab 		Wasserstein over Wasserstein for Gaussian mixtures
Wasserstein over Wasserstein for Gaussian mixtures
Open notebook · Open in Colab
## Dual Problem
Discrete Kantorovich dual potentials
Discrete Kantorovich dual potentials
Open notebook · Open in Colab 		Continuous Kantorovich dual potentials
Continuous Kantorovich dual potentials
Open notebook · Open in Colab 		Discrete c-transform lower envelopes
Discrete c-transform lower envelopes
Open notebook · Open in Colab
Concave closures from hard c-transforms
Concave closures from hard c-transforms
Open notebook · Open in Colab 		Auction algorithm progression
Auction algorithm progression
Open notebook · Open in Colab
## Semi-discrete and $W_1$
Semi-discrete Laguerre cells
Semi-discrete Laguerre cells
Open notebook · Open in Colab 		Lloyd quantization of a continuous density
Lloyd quantization of a continuous density
Open notebook · Open in Colab 		Graph Beckmann flow for W1
Graph Beckmann flow for W1
Open notebook · Open in Colab
## Divergences and Dual Norms
Integral probability metric witnesses
Integral probability metric witnesses
Open notebook · Open in Colab 		Generator functions for phi-divergences
Generator functions for phi-divergences
Open notebook · Open in Colab
## Entropic Regularization: Sinkhorn Algorithm
Entropic regularization on a transport polytope
Entropic regularization on a transport polytope
Open notebook · Open in Colab 		Marginal constraints during Sinkhorn scaling
Marginal constraints during Sinkhorn scaling
Open notebook · Open in Colab 		Dense Sinkhorn marginal scaling
Dense Sinkhorn marginal scaling
Open notebook · Open in Colab
Entropic plans as epsilon changes
Entropic plans as epsilon changes
Open notebook · Open in Colab 		Sinkhorn potentials along the iteration
Sinkhorn potentials along the iteration
Open notebook · Open in Colab 		Sinkhorn marginal error rates
Sinkhorn marginal error rates
Open notebook · Open in Colab
Path-space Brownian bridges for Sinkhorn couplings
Path-space Brownian bridges
Open notebook · Open in Colab 		Sinkhorn dual potentials as epsilon changes
Sinkhorn dual potentials as epsilon changes
Open notebook · Open in Colab 		Entropic couplings as epsilon changes
Entropic couplings as epsilon changes
Open notebook · Open in Colab
Soft c-transforms as epsilon decreases
Soft c-transforms as epsilon decreases
Open notebook · Open in Colab 		Regularized couplings and entropy choice
Regularized couplings and entropy choice
Open notebook · Open in Colab 		Sinkhorn debiasing by point optimization
Sinkhorn debiasing by point optimization
Open notebook · Open in Colab
## Entropic Regularization: Convergence
Empirical fluctuations of regularized losses
Empirical fluctuations of regularized losses
Open notebook · Open in Colab
## Generalized Wasserstein Distances
Unbalanced OT and KL mass relaxation
Unbalanced OT and KL mass relaxation
Open notebook · Open in Colab 		Unbalanced OT and marginal divergences
Unbalanced OT and marginal divergences
Open notebook · Open in Colab 		Sliced Wasserstein projections
Sliced Wasserstein projections
Open notebook · Open in Colab
Min-sliced lifted transport plan
Min-sliced lifted transport plan
Open notebook · Open in Colab 		Linear OT tangent coordinates
Linear OT tangent coordinates
Open notebook · Open in Colab 		Spectral gauges of displacement covariances
Spectral gauges of displacement covariances
Open notebook · Open in Colab
## Generalized OT Problems
Wasserstein barycenters of four shapes
Wasserstein barycenters of four shapes
Open notebook · Open in Colab 		Gaussian covariance barycenters
Gaussian covariance barycenters
Open notebook · Open in Colab 		Metric learning as cost deformation
Metric learning as cost deformation
Open notebook · Open in Colab
Forward OT solutions for bilinear logo costs
Forward OT solutions for bilinear logo costs
Open notebook · Open in Colab 		Inverse OT gap loss on Gaussian mixtures
Inverse OT gap loss on Gaussian mixtures
Open notebook · Open in Colab 		Weak OT and barycentric projection
Weak OT and barycentric projection
Open notebook · Open in Colab
## Beyond Comparing Measures
Positive vector-valued coupled transport
Positive vector-valued coupled transport
Open notebook · Open in Colab 		Positive matrix-valued coupled transport
Positive matrix-valued coupled transport
Open notebook · Open in Colab 		Gromov-Wasserstein matching of isometric shapes
Gromov-Wasserstein matching of isometric shapes
Open notebook · Open in Colab
Gromov-Wasserstein distortion for non-isometric shapes
Gromov-Wasserstein distortion for non-isometric shapes
Open notebook · Open in Colab 		Fused Gromov-Wasserstein: features versus geometry
Fused Gromov-Wasserstein: features versus geometry
Open notebook · Open in Colab
## Dynamic Optimal Transport
Benamou-Brenier geodesic
Benamou-Brenier geodesic
Open notebook · Open in Colab 		One-dimensional balanced and unbalanced dynamic geodesics
One-dimensional balanced and unbalanced dynamic geodesics
Open notebook · Open in Colab
## Wasserstein Gradient Flows
JKO steps for the entropy flow
JKO steps for the entropy flow
Open notebook · Open in Colab 		Heat flow and porous-medium powers
Heat flow and porous-medium powers
Open notebook · Open in Colab 		Interaction-energy particle flow
Interaction-energy particle flow
Open notebook · Open in Colab
Three Fokker-Planck representations
Three Fokker-Planck representations
Open notebook · Open in Colab 		Particle count for squared-MMD flow
Particle count for squared-MMD flow
Open notebook · Open in Colab
Particle trajectories for different discrepancy geometries
Particle trajectories for different discrepancy geometries
Open notebook · Open in Colab 		Homogeneous ReLU mean-field flow
Homogeneous ReLU mean-field flow
Open notebook · Open in Colab
## Generative Models via Transportation
Flow matching: stochastic interpolants
Flow matching: stochastic interpolants
Open notebook · Open in Colab 		One-dimensional diffusion bridge
One-dimensional diffusion bridge
Open notebook · Open in Colab 		Two-dimensional diffusion bridge
Two-dimensional diffusion bridge
Open notebook · Open in Colab
Diffusion trajectories versus OT rays
Diffusion trajectories versus OT rays
Open notebook · Open in Colab 		Diffusion schedule comparison
Diffusion schedule comparison
Open notebook · Open in Colab 		Drifting fields for a small particle generator
Drifting fields for a small particle generator
Open notebook · Open in Colab
Gaussian closure of a Wasserstein flow
Gaussian closure of a Wasserstein flow
Open notebook · Open in Colab
## Roadmap and Archive Archived or exploratory notebooks are intentionally omitted from this gallery. See [`figures.md`](figures.md) for the figure roadmap and [`removed/`](removed/) for retired notebooks.