Research map / Probabilistic and scientific modeling / Dynamical systems
Go With the Flow: Fast Diffusion for Gaussian Mixture Models
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes a training-free method that solves Schrödinger bridges (and multi-marginal momentum SBs) between Gaussian mixture models by mixing closed-form Gaussian bridge policies weighted by a linear program over component transport plans.
Problem
Solving Schrödinger bridges between distributions available as samples is expensive with neural training, even for low-dimensional problems; existing lightweight solvers (LightSB, LightSB-M) use non-convex optimization that can converge to local optima.
Approach
Decompose the GMM-to-GMM bridge into a mixture of conditional Gaussian-to-Gaussian bridges (closed form via covariance steering/SDP), with component-level transport plan obtained by solving a linear program whose cost is the per-pair Gaussian bridge cost, giving an upper bound on the true cost.
Key results
- Man-to-woman FID 3.04 for GMMflow vs 4.94 for LSB, roughly 40% better FID on image translation.
- Multi-marginal scRNA-seq: outperforms DMSB, NSBL, MIOFlow by one order of magnitude in MMD, with about 8 minutes of CPU training.
- Training takes 63% less time than LightSB-based baselines in the image translation task.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GMMflow instead of LSBM | Man-to-Woman image translation · Man-to-Woman | FID: 4.98 -> 3.04 | Helped |
| Use GMMflow instead of LSBM | Man-to-Woman image translation · Man-to-Woman | ALAE-BW: 28.3 -> 9.3 | Helped |
| Use GMMflow instead of LSBM | Man-to-Woman image translation · Man-to-Woman | transport cost: 8.18 -> 9.05 | Hurt |
| Use GMMflow instead of LSBM | Adult-to-Child image translation · Adult-to-Child | FID: 6.61 -> 3.50 | Helped |
| Use GMMflow instead of LSBM | Adult-to-Child image translation · Adult-to-Child | ALAE-BW: 30.99 -> 8.54 | Helped |
| Use GMMflow instead of LSBM | Adult-to-Child image translation · Adult-to-Child | transport cost: 8.19 -> 9.33 | Hurt |
| Use GMMflow instead of neural baselines | Multi-marginal momentum Schrödinger Bridge · scRNA-seq, 4 predicted time marginals | MMD | Helped |
| Use GMMflow instead of neural baselines | Multi-marginal momentum Schrödinger Bridge · scRNA-seq, 4 predicted time marginals | SWD | Mixed |
| Use GMMflow instead of lightweight SB solvers | Image-to-image translation · Man-to-Woman and Adult-to-Child | training time: 63% less time | Helped |
Surprising findings
- Improved FID and ALAE-BW come with a slightly higher average transport cost than the baselines.
Limitations
- Dependence on GMM marginals limits applicability to very high-dimensional problems.
- Upper bound on cost is tight only when conditional densities are well separated.
- Transport cost is higher than baselines in image translation.
Experimental setup
Datasets: FFHQ scRNA-seq dataset (from cited work)
Benchmarks: FFHQ man-to-woman and adult-to-child translation scRNA-seq multi-marginal trajectory 2D Gaussian-to-8-Gaussians SB
Metrics: FID ALAE-BW transport cost SWD MMD
Baselines: LightSB LightSB-M DSB DSBM DMSB NSBL MIOFlow
Builds on: Diffusion Schrödinger Bridge Matching Light-SB Light-SB Matching Gaussian Schrödinger bridge closed form Covariance steering
Closest papers by meaning
- Generalized Schrödinger Bridge Matching (ICLR 2024 · similarity 0.92)
- Learning non-equilibrium diffusions with Schrödinger bridges: from exactly solvable to simulation-free (NeurIPS 2025 · similarity 0.91)
- Momentum Multi-Marginal Schrödinger Bridge Matching (NeurIPS 2025 · similarity 0.91)
- Variational Schrödinger Diffusion Models (ICML 2024 · similarity 0.90)
- Finding Local Diffusion Schrodinger Bridge using Kolmogorov-Arnold Network (CVPR 2025 · similarity 0.89)
- Feedback Schrödinger Bridge Matching (ICLR 2025 · similarity 0.89)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.