Research map / Probabilistic and scientific modeling / Variational and generative sampling
Stream-level Flow Matching with Gaussian Processes
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Extends conditional flow matching to the stream level by modeling latent stochastic streams between endpoints as Gaussian processes, preserving simulation-free training and enabling correlated observations.
Problem
Standard conditional flow matching conditions only on endpoints or target samples, which yields high-variance marginal vector field estimates and cannot naturally incorporate multiple correlated observations such as time series or grouped data.
Approach
Define conditional probability paths along latent streams modeled as Gaussian processes conditioned on endpoints (and optional intermediate observations); the GP's velocity is also a GP, so joint (stream, velocity) samples remain available in closed form, giving a stream-level CFM loss that is simulation-free and reduces estimator variance via kernel-controlled stochasticity.
Key results
- On CIFAR-10, GP-I-CFM reaches FID 3.62 (SE 0.008) versus 3.75 for I-CFM.
- On MNIST over 100 training runs, GP-OT-CFM gives FID 42.99 versus 44.50 for I-CFM and KID 0.0031 versus 0.0040.
- On the 2-Gaussian toy task, GP-OT-CFM achieves W2 1.35 versus 1.43 for OT-CFM and 1.54 for I-CFM.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace linear streams with GP streams using independent endpoint coupling | I-CFM · 2-Gaussian mixture from standard Gaussian | W2 distance: 1.54 -> 1.51 | Helped |
| Add GP streams to OT endpoint coupling | OT-CFM · 2-Gaussian mixture from standard Gaussian | W2 distance: 1.43 -> 1.35 | Helped |
| Use increasing rather than no noise in GP streams (ablation) | GP-I-CFM · 2-Gaussian mixture from standard Gaussian | W2 distance: 0.269 -> 0.243 | Helped |
| Add constant noise to GP streams rather than no noise (ablation) | GP-I-CFM · 2-Gaussian mixture from standard Gaussian | W2 distance: 0.269 -> 0.305 | Hurt |
| Use decreasing rather than no noise in GP streams (ablation) | GP-I-CFM · 2-Gaussian mixture from standard Gaussian | W2 distance: 0.269 -> 0.329 | Hurt |
| Add constant noise to GP streams (ablation) | GP-I-CFM · 2-Gaussian to 2-Gaussian | W2 distance: 0.681 -> 0.350 | Helped |
| Use decreasing noise in GP streams (ablation) | GP-I-CFM · 2-Gaussian to 2-Gaussian | W2 distance: 0.681 -> 0.413 | Helped |
| Use increasing noise in GP streams (ablation) | GP-I-CFM · 2-Gaussian to 2-Gaussian | W2 distance: 0.681 -> 0.411 | Helped |
| Replace linear streams with GP streams using independent endpoint coupling | I-CFM · MNIST | KID: 0.0040 -> 0.0032 | Helped |
| Add GP streams to OT endpoint coupling | OT-CFM · MNIST | FID: 44.21 -> 42.99 | Helped |
| Replace linear streams with GP streams using independent endpoint coupling | I-CFM · CIFAR-10 | FID: 3.75 -> 3.62 | Helped |
| Add GP streams to OT endpoint coupling | OT-CFM · CIFAR-10 | FID: 3.74 -> 3.75 | Hurt |
Surprising findings
- Injecting noise at t=0 worsened estimation in the single-source setting, while noise near t=1 helped with small target samples.
- Combining OT coupling with GP streams did not improve CIFAR-10 FID or sample generation time over GP-I-CFM alone.
Limitations
- GP-stream training costs more per iteration than linear interpolants, roughly 17% slower on CIFAR-10.
- Gains on CIFAR-10 are modest and OT coupling adds little in high dimensions because minibatch OT is poor.
- Only a single-endpoint-pair stream and independent-across-dimensions GP are used in experiments.
Experimental setup
Datasets: MNIST CIFAR-10 HWD+ LFP mouse brain local field potential 2-Gaussian mixture simulations
Benchmarks: MNIST CIFAR-10 HWD+ 2-Gaussian mixture simulation
Metrics: 2-Wasserstein distance kernel inception distance Fréchet inception distance sample generation time
Baselines: I-CFM OT-CFM stochastic interpolants multimarginal stochastic interpolants
Builds on: conditional flow matching stochastic interpolants optimal transport conditional flow matching rectified flow guided flow matching
Closest papers by meaning
- Reflected Flow Matching (ICML 2024 · similarity 0.89)
- Flow Matching Neural Processes (NeurIPS 2025 · similarity 0.88)
- Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting (ICLR 2025 · similarity 0.88)
- MissPath-FM: Flow Matching with Structured Priors for Partially Observed Time Series (NeurIPS 2026 · similarity 0.88)
- An Error Analysis of Flow Matching for Deep Generative Modeling (ICML 2025 · similarity 0.88)
- Improving Function Space Flow Matching with Kernel Optimal Transport (NeurIPS 2026 · similarity 0.88)
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