Research map / Image generation / Autoregressive and latent generation
Lost in Latent Space: An Empirical Study of Latent Diffusion Models for Physics Emulation
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.
Empirical study of latent-space diffusion and neural-solver emulators for three TheWell fluid/astrophysics datasets, showing emulation accuracy is robust to autoencoder compression up to 1000x and diffusion emulators beat deterministic solvers.
Problem
Diffusion-based physics emulators are too expensive at inference; it is unclear how much latent-space compression can be applied to dynamical system emulation without hurting accuracy.
Approach
Train convolutional autoencoders with a saturating latent bound (instead of KL) and a transformer latent diffusion emulator with temporal bundling, systematically varying compression rate and comparing against pixel-space and deterministic latent neural solvers.
Key results
- Latent diffusion emulators remain accurate across compression rates up to 1280x on Euler (VRMSE ~0.37-0.40 at lead 61:100 for rates 80-1280), with VRMSE not degrading and sometimes improving on RB.
- Diffusion-based emulators are consistently more accurate than latent neural solvers; e.g., Euler 61:100 VRMSE 0.395 (diffusion, rate 80) vs 0.500 (neural solver, rate 80).
- Generating and decoding a 100-step Euler trajectory takes about 3 seconds on one A100, versus roughly 1 CPU-hour for the numerical simulator.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| increase latent compression from 80 to 320 (ablation) | Latent diffusion · Euler Multi-Quadrants 61:100 | VRMSE: 0.395 -> 0.371 | Helped |
| increase latent compression from 320 to 1280 (ablation) | Latent diffusion · Euler Multi-Quadrants 61:100 | VRMSE: 0.371 -> 0.400 | Hurt |
| increase latent compression from 64 to 1024 (ablation) | Latent diffusion · Rayleigh-Bénard 61:180 | VRMSE: 0.704 -> 0.670 | Helped |
| increase latent compression from 48 to 768 (ablation) | Latent diffusion · Turbulence Gravity Cooling 21:50 | VRMSE: 0.673 -> 0.694 | Hurt |
| use latent diffusion instead of the pixel-space neural solver | Euler Multi-Quadrants emulator · Euler Multi-Quadrants 61:100 | VRMSE: 1.102 -> 0.395 | Helped |
| use latent diffusion instead of the latent neural solver | Euler Multi-Quadrants emulator (compression 80) · Euler Multi-Quadrants 61:100 | VRMSE: 0.500 -> 0.395 | Helped |
| use latent diffusion instead of the latent neural solver | Rayleigh-Bénard emulator (compression 64) · Rayleigh-Bénard 61:180 | VRMSE: 0.968 -> 0.704 | Helped |
| use latent diffusion instead of the latent neural solver | Turbulence Gravity Cooling emulator (compression 48) · Turbulence Gravity Cooling 21:50 | VRMSE: 0.826 -> 0.673 | Helped |
| add near-identity initialization to downsampling and upsampling layers (ablation) | Autoencoder trained with Adam · Rayleigh-Bénard validation, epoch 1000 | MAE: 0.017 -> 0.014 | Helped |
| replace Adam with PSGD while retaining near-identity initialization (ablation) | Autoencoder · Rayleigh-Bénard validation, epoch 1000 | MAE: 0.014 -> 0.011 | Helped |
| vary context length among 1, 2, and 3 (ablation) | Latent diffusion · Euler Multi-Quadrants | VRMSE: 0.393, 0.383, 0.389 | No clear effect |
Surprising findings
- Emulation accuracy is robust to, and sometimes improves with, latent compression even when autoencoder reconstruction degrades markedly.
- Latent-space emulators outperform the pixel-space neural solver despite using fewer parameters and less training compute.
Limitations
- Evaluated only on three fluid/astrophysics datasets from TheWell; generalization to chemical or quantum systems untested.
- No error bars; retraining for statistical significance was not done.
- Suspected overfitting at high compression indicated by decreasing spread-skill ratio.
Experimental setup
Datasets: Euler Multi-Quadrants (TheWell) Rayleigh-Benard (TheWell) Turbulence Gravity Cooling (TheWell)
Benchmarks: TheWell Euler TheWell Rayleigh-Benard TheWell Turbulence Gravity Cooling
Metrics: VRMSE power spectrum RMSE spread-skill ratio sliced earth mover's distance Wasserstein distance
Baselines: pixel-space neural solver latent neural solver pixel-space diffusion FNO U-Net numerical simulator (Clawpack)
Builds on: latent diffusion models Rectified flow MCVD Ohana et al. 2024 (The Well) DC-AE (deep compression autoencoder)
Closest papers by meaning
- Wavelet Flow Matching for Multi-Scale Physics Emulation (NeurIPS 2026 · similarity 0.88)
- Text2PDE: Latent Diffusion Models for Accessible Physics Simulation (ICLR 2025 · similarity 0.87)
- PhysCtrl: Generative Physics for Controllable and Physics-Grounded Video Generation (NeurIPS 2025 · similarity 0.87)
- LaMo: Self-Supervised Latent Motion Priors for Physical Realism in Video Generation (NeurIPS 2026 · similarity 0.87)
- Plug-and-Play Diffusion Distillation (CVPR 2024 · similarity 0.87)
- Improving the Diffusability of Autoencoders (ICML 2025 · similarity 0.87)
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.