Research map / Probabilistic and scientific modeling / Variational and generative sampling
Neural Guided Diffusion Bridges
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Proposes neural guided diffusion bridges: a guided proposal with a learned neural drift correction, trained variationally by minimizing KL to the true bridge, giving cheap independent bridge samples without MCMC or score matching.
Problem
Simulating diffusion bridges (diffusion processes conditioned on endpoint observations) is hard: guided proposals need costly MCMC/SMC, and score-matching methods learn from unconditioned samples that rarely reach rare-event endpoints.
Approach
Augment the guided proposal (linear auxiliary process guiding term) with a learnable bounded neural drift correction sigma*theta(t,x), trained by minimizing KL divergence from the variational bridge to the true bridge using samples from the learned bridge itself (conditional samples, not unconditioned ones).
Key results
- On Brownian and OU bridges, training loss converges to the analytical lower bound on KL divergence, showing the learned bridge is close to the true bridge.
- Neural bridge has 921 parameters on OU vs 21,969 for adjoint forward and 26,353 for score matching, and trains in 44.12s vs 162.68s and 65.55s.
- On the cell model rare event and multimodal cases, the neural bridge matches guided proposal performance while score matching and adjoint methods fail to capture modes; the rare-event forward sampling yielded zero hits in 100,000 samples.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add a learned correction drift to the guided proposal | Cell diffusion bridge · Cell diffusion, normal event | conditional trajectory fidelity | No clear effect |
| Use the learned correction drift instead of score matching | Cell diffusion bridge · Cell diffusion, rare event | trajectory fidelity | Helped |
| Use the learned correction drift instead of the adjoint forward approach | Cell diffusion bridge · Cell diffusion, rare event | trajectory fidelity | Helped |
| Use the learned correction drift instead of score matching | Cell diffusion bridge · Cell diffusion, multi-modality | marginal distribution fidelity | Helped |
| Use the learned correction drift instead of the adjoint forward approach | Cell diffusion bridge · Cell diffusion, multi-modality | marginal distribution fidelity | Helped |
| Add a learned correction drift to the guided proposal | FitzHugh-Nagumo bridge · FHN, normal event | trajectory fidelity | No clear effect |
| Add a learned correction drift to the guided proposal | FitzHugh-Nagumo bridge · FHN, rare event | trajectory fidelity | Mixed |
| Use the learned correction drift rather than the linear guided proposal alone | Stochastic landmark matching · Stochastic landmark matching | endpoint-reaching performance | Helped |
| Use the learned correction drift rather than score matching | Neural guided bridge · OU (d=1) | training time: 65.55s -> 44.12s | Helped |
| Use the learned correction drift rather than score matching | Neural guided bridge · Cell (d=2) | training time: 103.38s -> 94.79s | Helped |
| Use the learned correction drift rather than score matching | Neural guided bridge · Landmark (d=20) | training time: 353.05s -> 122.48s | Helped |
Surprising findings
- Adjoint forward and score matching fail to capture multimodal bridge marginals, while the guided proposal and neural bridge agree.
- Forward sampling of 100,000 unconditioned paths yielded no samples near the rare-event endpoint, so the unconditioned approach cannot provide references there.
Limitations
- Variational KL minimization is mode-seeking, possibly missing modes compared with multiple MCMC chains.
- Backpropagation through the whole SDE solver scales linearly in time steps and quadratically in dimension; evaluated only on moderate-dimensional problems.
- Neural network approximation error grows outside regions covered by training data.
Experimental setup
Datasets: simulated diffusion trajectories
Benchmarks: Brownian bridge analytical lower bound Ornstein-Uhlenbeck bridge analytical lower bound cell diffusion model FitzHugh-Nagumo model stochastic landmark matching
Metrics: training loss vs analytical lower bound marginal density comparison parameter count training time
Baselines: guided proposal score matching bridge simulation adjoint forward bridge
Builds on: guided proposal preconditioned Crank-Nicolson Doob h-transform score matching bridge simulation
Closest papers by meaning
- Underdamped Diffusion Bridges with Applications to Sampling (ICLR 2025 · similarity 0.89)
- Improved sampling via learned diffusions (ICLR 2024 · similarity 0.89)
- Stochastic Optimal Control for Diffusion Bridges in Function Spaces (NeurIPS 2024 · similarity 0.87)
- Diffusion Bridge Implicit Models (ICLR 2025 · similarity 0.87)
- Rethinking Losses for Diffusion Bridge Samplers (NeurIPS 2025 · similarity 0.87)
- Conditioning Diffusions Using Malliavin Calculus (ICML 2025 · similarity 0.87)
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