Research map / Probabilistic and scientific modeling / Variational and generative sampling
Generative Modeling by Value-Driven Transport
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Casts dynamic optimal transport as a discrete-time control LP and trains value-driven transport (VDT) generative policies via a simulation-free primal-dual method with a single value network.
Problem
Generative modeling as measure transport: learning transport maps between source and target distributions with minimal movement cost, without relying on diffusion/flow/Schrödinger-bridge machinery or simulated trajectories during training.
Approach
Formulate discrete-time dynamic OT as an LP over occupancy measures whose dual variables are the optimal value function; parametrize primal particles by stochastic-interpolant initialization updated by Wasserstein gradient descent, and generate via gradient steps of the value function (VDT policy), enabling few-step generation.
Key results
- On 2D benchmarks, OT-initialized VDT (VDT+) gives reasonable accuracy after a single generation step, and results with 10 steps are nearly identical to 100 steps (tenfold speedup).
- On MNIST and EMNIST translation, few-step generation with H_test=10 versus training horizon H=100 retains quality.
- Classifier-free guidance on conditional MNIST improves sample quality at the cost of diversity, as in diffusion models.
Surprising findings
- Few-step (10-step) generation matches 100-step generation quality, indicating near-straight transport paths.
Limitations
- Method not yet scaled to challenging generative tasks; experiments limited to small-scale 2D and MNIST-level data.
- No established best practices for the new primal-dual training procedure.
Experimental setup
Datasets: moons scurve 8gauss MNIST EMNIST
Benchmarks: 2D moons/scurve/8gauss MNIST deblurring EMNIST-to-MNIST translation MNIST conditional generation
Metrics: Wasserstein-2 distance path energy
Baselines: conditional flow matching rectified flow c-rectified flow Schrödinger bridge methods
Builds on: conditional flow matching rectified flow classifier-free guidance Benamou-Brenier dynamic optimal transport Wasserstein gradient descent
Closest papers by meaning
- Dynamic Conditional Optimal Transport through Simulation-Free Flows (NeurIPS 2024 · similarity 0.87)
- Multimarginal Generative Modeling with Stochastic Interpolants (ICLR 2024 · similarity 0.87)
- Stochastic Interpolants with Data-Dependent Couplings (ICML 2024 · similarity 0.86)
- Stochastic Optimal Control for Diffusion Bridges in Function Spaces (NeurIPS 2024 · similarity 0.86)
- One-Shot Generative Flows: Existence and Obstructions (NeurIPS 2026 · similarity 0.86)
- Generative Modeling with Phase Stochastic Bridge (ICLR 2024 · similarity 0.86)
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