Calendar

Part I · Instructor lectures

Mon Sep 7 · No class

Labor Day (university holiday). First class meets Sep 14.

Mon Sep 14 · Tour of Optimal Transport and Flow Matching · Slides

Released Preparatory homework (10% of the grade)

Course intro & logistics. Historical views and main results. Overview of recent advances in the field.

Background reading:

• Computational Optimal Transport, §1–2
• An Introduction to Flow Matching and Diffusion Models, §1–2

Mon Sep 21 · Duality in computational optimal transport

Due Preparatory homework, at the start of class

Whiteboard session The Kantorovich linear program and its dual, strong duality, and the Kantorovich–Rubinstein theorem. Entropic regularization and the Sinkhorn algorithm.

Background reading:

• Computational Optimal Transport, §3–4

Mon Sep 28 · A dynamic view on distribution morphing

Due Paper presentation sign-up, on Brightspace

Whiteboard session Flows of vector fields and the continuity equation; dynamic optimal transport and the Benamou–Brenier formulation. Flow models, conditional probability paths, the marginalization trick, and the flow matching objective.

Background reading:

• Computational Optimal Transport, §7
• An Introduction to Flow Matching and Diffusion Models, §3,§5,§6

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Part II · Reading group

Papers in this part are presented by students in the reading group. See Role-play Seminar for how the sessions are organized, the roles, and expectations.

Mon Oct 5 · Supervised training of Monge maps

Due Project team registration, on Brightspace

Papers to present:

• Supervised Training of Conditional Monge Maps (Bunne et al., 2022)
• Monge Gap (Uscidda & Cuturi, 2023)

Mon Oct 12 · No class

Fall Break (university holiday).

Wed Oct 14 · Alternate optimal transport problems

Legislative Monday: classes meet on a Monday schedule.

Papers to present:

• Gromov–Wasserstein Averaging of Kernel and Distance Matrices (Peyré et al., 2016)
• CO-Optimal Transport (Redko et al., 2020)

Mon Oct 19 · Conditional generation and guidance

Papers to present:

• Guided Flows for Generative Modeling and Decision Making (Zheng et al., 2023)
• CFG-Zero*: Improved Classifier-Free Guidance (Fan et al., 2025)

Mon Oct 26 · Flow matching on structured domains

Papers to present:

• Riemannian Flow Matching on General Geometries (Chen & Lipman, 2023)
• Discrete Flow Matching (Gat et al., 2024)

Mon Nov 2 · Amortizing maps and flows over distributions

Due Project check-in, on Brightspace

Papers to present:

• Wasserstein Wormhole: Scalable Optimal Transport Distance with Transformers (Haviv et al., 2024)
• Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold (Atanackovic et al., 2025)

Mon Nov 9 · Fast sampling from flow-matching models

Papers to present:

• Flow Map Matching (Boffi et al., 2024)
• Mean Flow (Geng et al., 2025)

Mon Nov 16 · OT couplings inside flow matching

Papers to present:

• OT-CFM: Conditional Flow Matching with minibatch OT (Tong et al., 2023)
• MMFM: Flow Matching across time and conditions (Rohbeck et al., 2025)

Mon Nov 23 · Unbalancedness in transport maps

Papers to present:

• Unbalanced Minibatch Optimal Transport; Applications to Domain Adaptation (Fatras et al., 2021)
• Unbalancedness in Neural Monge Maps (Eyring et al., 2024)

Mon Nov 30 · Applications

Papers to present:

• GENOT: Generative Entropic Neural Optimal Transport (Klein et al., 2024)
• MusicFlow: Cascaded Flow Matching for Text Guided Music Generation (Prajwal et al., 2024)

Mon Dec 7 · Final project poster session

Due Final project: poster

Every team presents a poster in class and uploads it on Brightspace. See Project Logistics.

Mon Dec 14 · Guest talk

Virtual guest talk, speaker to be announced. Last day of classes.