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

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

Released Preparatory homework (10% of the grade)

Background reading & Reference texts for the course. These are the two reference documents for the field.

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

Mon Sep 21 · Duality

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

Due Preparatory homework — at the start of class

Background reading:

• Computational Optimal Transport — §3–4

Mon Sep 28 · A dynamic view on distribution morphing

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

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

Due Project — preliminary proposal

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

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 I: single-cell biology

Papers to present:

• Optimal-Transport Analysis of Single-Cell Gene Expression / Waddington-OT (Schiebinger et al., 2019)
• GENOT: Generative Entropic Neural Optimal Transport (Klein et al., 2024)

Mon Dec 7 · Applications II: music generation

Papers to present:

• MusicFlow: Cascaded Flow Matching for Text Guided Music Generation (Prajwal et al., 2024)
• Auto-Regressive vs Flow-Matching: a Comparative Study of Modeling Paradigms for Text-to-Music Generation (Tal et al., 2025)

Mon Dec 14 · Final project session

Due Final project — write-up & presentation

Last day of classes. See Project Logistics.