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Text2PDE: Latent Diffusion Models for Accessible Physics Simulation
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Applies latent diffusion models with a kernel-integral mesh autoencoder to generate full spatio-temporal PDE trajectories, conditioned on first frames or text prompts, scaling to ~3B parameters.
Problem
Neural PDE solvers are autoregressive, accumulate error, struggle with arbitrary discretizations, and are inaccessible to non-experts; the paper asks how to generate PDE solutions on arbitrary meshes and condition them on text.
Approach
A mesh autoencoder that maps arbitrarily discretized PDE data to a uniform latent grid via local kernel integrals (and back), enabling a DiT-based latent diffusion model to generate entire trajectories at once, conditioned on the first frame or a text prompt encoded by a fine-tuned RoBERTa.
Key results
- On Cylinder Flow, LDM-M-FF reaches relative L2 0.1309 vs. 0.2445 for GINO and 0.2617 for MGN, with flops comparable to GINO.
- On 3D Turbulence, LDM-FF achieves L2 0.602 and D_TKE 5.630, beating FNO, FactFormer, and Dil-ResNet.
- On Buoyancy-Driven Flow, LDM-L-FF reaches L2 0.2728 vs. 0.3050 for the Unet baseline, with text conditioning at 0.2944 (re-solved evaluation).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Condition on the first frame instead of text | LDM · Cylinder Flow | L2 loss: 0.1796 -> 0.1522 (Small); 0.1476 -> 0.1309 (Medium) | Helped |
| Increase model size from Small to Large | LDM-FF · Buoyancy-Driven Flow | L2 loss: 0.3459 -> 0.2728 | Helped |
| Add GAN training (ablation) | Cylinder Flow autoencoder · Cylinder Flow | L1 reconstruction loss: .0340 -> .0311 | Helped |
| Add LPIPS perceptual loss (ablation) | Cylinder Flow autoencoder · Cylinder Flow | L1 reconstruction loss: .0340 -> .0208 | Helped |
| Add GAN training (ablation) | Smoke Buoyancy autoencoder · Smoke Buoyancy | L1 reconstruction loss: .00535 -> .00916 | Hurt |
| Add LPIPS perceptual loss (ablation) | Smoke Buoyancy autoencoder · Smoke Buoyancy | L1 reconstruction loss: .00535 -> .00938 | Hurt |
| Use KL penalty 2e-7 instead of 5e-6 (ablation) | Smoke Buoyancy autoencoder · Smoke Buoyancy | L1 reconstruction loss: 0.378 -> 0.239 | Helped |
| Increase mesh aggregation ball radius (ablation) | Cylinder Flow mesh autoencoder · Cylinder Flow | L1 reconstruction loss: .0148 -> .0138 | Helped |
| Replace proposed mesh autoencoder with GNN (ablation) | Cylinder Flow autoencoder · Cylinder Flow | L1 reconstruction loss: .011 -> .382 | Hurt |
| Replace proposed mesh autoencoder with neural field (ablation) | Cylinder Flow autoencoder · Cylinder Flow | L1 reconstruction loss: .011 -> .171 | Hurt |
| Replace Unet backbone with DiT (ablation) | LDM, first-frame conditioning · Cylinder Flow | L1 loss: 0.0416 -> 0.0385 | Helped |
| Replace Unet backbone with DiT (ablation) | LDM, text conditioning · Cylinder Flow | L1 loss: 0.0492 -> 0.0404 | Helped |
Surprising findings
- Text conditioning nearly matches first-frame conditioning on cylinder flow despite using roughly 1000x less conditioning data.
- GAN and LPIPS perceptual losses improved reconstruction on cylinder flow but not on smoke buoyancy, and were omitted from main results.
Limitations
- Diffusion inference is slower than conventional solvers at default step counts, and the full-rollout approach fixes the temporal horizon.
- LLM captioning of smoke buoyancy initial conditions can hallucinate, degrading text-conditioned results.
- Generated 3D turbulence samples smooth high-frequency features.
Experimental setup
Datasets: 2D cylinder flow (Reynolds 100-1500) 2D buoyancy-driven smoke flow 3D turbulence around geometric objects
Benchmarks: Cylinder Flow Buoyancy-Driven Flow 3D Turbulence
Metrics: relative L2 loss inference time (s) flops log-TKE distance D_TKE
Baselines: GINO MeshGraphNet OFormer FNO Unet Dil-ResNet ACDM FactFormer FNO3D
Builds on: latent diffusion models diffusion transformer adaLN-Zero classifier-free guidance DDIM
Closest papers by meaning
- Ultra Fast PDE Solving via Physics Guided Few-step Diffusion (NeurIPS 2026 · similarity 0.92)
- Breakeven complexity: A new perspective on neural partial differential equation solvers (NeurIPS 2026 · similarity 0.90)
- PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems (ICLR 2025 · similarity 0.89)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.89)
- Learning a Neural Solver for Parametric PDEs to Enhance Physics-Informed Methods (ICLR 2025 · similarity 0.89)
- P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics (NeurIPS 2024 · similarity 0.89)
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