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Consistency Models for Scalable and Fast Simulation-Based Inference
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Proposes consistency model posterior estimation (CMPE), a conditional consistency-model sampler for simulation-based inference that enables few-step posterior sampling with unconstrained architectures.
Problem
Neural posterior estimation needs expressive unconstrained architectures but diffusion/flow-matching posterior samplers are slow at inference, and existing flow-based SBI methods are bijectivity-constrained.
Approach
Adapt consistency models (direct consistency training, no teacher diffusion model) to conditional posterior estimation with a conditioning observation x, using hyperparameters tuned for low-dimensional SBI, so that posterior draws take one or few network passes.
Key results
- On the Gaussian mixture benchmark CMPE outperforms 1000-step FMPE in C2ST while being about 75x faster.
- On Fashion MNIST with a naive architecture, CMPE (2 steps) achieves RMSE 0.388 vs FMPE 0.836 with 2,000 training images, at 0.3ms vs 15.4ms per draw.
- On the tumor spheroid model, CMPE with 30 steps achieves the lowest max ECE (0.018) among methods, at 18.33s for 2000 samples vs 500.90s for FMPE with 1000 steps.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CMPE instead of FMPE with the naive architecture | Fashion MNIST denoising · Fashion MNIST, naive architecture, 2,000 images | RMSE: 0.836 -> 0.388 | Helped |
| Use CMPE instead of FMPE with the naive architecture | Fashion MNIST denoising · Fashion MNIST, naive architecture, 60,000 images | MMD (×10⁻³): 95.26 ± 1.21 -> 57.90 ± 1.59 | Helped |
| Use CMPE instead of FMPE with the U-Net architecture | Fashion MNIST denoising · Fashion MNIST, U-Net, 60,000 images | RMSE: 0.217 -> 0.238 | Hurt |
| Use CMPE instead of FMPE with the U-Net architecture | Fashion MNIST denoising · Fashion MNIST, U-Net, 60,000 images | time per draw: 565.8ms -> 0.5ms | Helped |
| Use CMPE instead of FMPE at 30 steps | Tumor spheroid growth · Tumor spheroid growth | Max ECE: 0.222 -> 0.018 | Helped |
| Use CMPE instead of FMPE at 30 steps | Tumor spheroid growth · Tumor spheroid growth | RMSE: 0.582 -> 0.577 | Helped |
| Increase CMPE sampling from 2 to 30 steps (ablation) | CMPE · Tumor spheroid growth | RMSE: 0.616 -> 0.577 | Helped |
| Increase CMPE sampling from 2 to 30 steps (ablation) | CMPE · Tumor spheroid growth | Max ECE: 0.064 -> 0.018 | Helped |
| Use U-Net instead of the naive architecture (ablation) | CMPE · Fashion MNIST, 2,000 images | RMSE: 0.388 -> 0.311 | Helped |
| Use U-Net instead of the naive architecture (ablation) | CMPE · Fashion MNIST, 2,000 images | MMD (×10⁻³): 102.09 ± 3.24 -> 18.49 ± 0.12 | Helped |
| Use U-Net instead of the naive architecture (ablation) | FMPE · Fashion MNIST, 2,000 images | RMSE: 0.836 -> 0.278 | Helped |
| Increase CMPE sampling steps beyond its best-performing range (ablation) | CMPE · Gaussian Mixture Model, Two Moons, and Inverse Kinematics | C2ST | Hurt |
Surprising findings
- C2ST performance is non-monotonic in the number of CMPE sampling steps, with a U-shaped relation and best results at about 10-20 steps.
- On gravitational wave inference (appendix), CMPE yields a pathologically underexpressive posterior compared to FMPE.
Limitations
- Consistency models do not provide tractable densities at arbitrary parameter values; only at posterior draws.
- Relation between number of sampling steps and posterior accuracy is non-monotonic, requiring a sweep over steps.
- Pathologically underexpressive posteriors on the gravitational wave experiment in the appendix.
Experimental setup
Datasets: Gaussian mixture model (simulated) Two Moons (simulated) inverse kinematics (simulated) Fashion MNIST tumor spheroid growth simulator GW150914 gravitational wave data
Benchmarks: Gaussian mixture model Two Moons inverse kinematics Fashion MNIST denoising tumor spheroid growth GW150914
Metrics: C2ST RMSE MMD ECE SBC sampling time
Baselines: affine coupling flow neural spline flow flow matching posterior estimation (FMPE)
Builds on: consistency models flow matching posterior estimation neural spline flows affine coupling flows rectified flow
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