Checkpoint/Restart (C/R) strategies are vital for fault tolerance in PDE-based scientific simulations, yet traditional checkpointing incurs significant I/O overhead. Lossy compression offers a scalable solution by reducing checkpoint data size, but conventional methods often lack control over physical invariants (e.g., energy), leading to instability such as oscillations or divergence in Partial Differential Equations (PDE) systems. This paper introduces a stability-preserving compression approach tailored for PDE simulations by explicitly controlling kinetic and potential energy perturbations to ensure stable restarts. Extensive experiments conducted across diverse PDE configurations demonstrate that our method maintains numerical stability with minimal error magnification—even across multiple checkpoint-restart cycles—outperforming state-of-the-art lossy compressors. Parallel evaluations on the Frontier supercomputer show up to 8.4× improvement in checkpoint write performance and 6.3× in read performance, while maintaining relative L2 errors ∼ 2e-6 throughout continued simulation. These results provide practical guidance for balancing compression accuracy, stability, and computational efficiency in large-scale PDE applications.

Generative models have demonstrated strong performance in conditional settings and can be viewed as a form of data compression, where the condition serves as a compact representation. However, their limited controllability and reconstruction accuracy restrict their practical application to data compression. In this work, we propose an efficient latent diffusion framework that bridges this gap by combining a variational autoencoder with a conditional diffusion model. Our method compresses only a small number of keyframes into latent space and uses them as conditioning inputs to reconstruct the remaining frames via generative interpolation, eliminating the need to store latent representations for every frame. This approach enables accurate spatiotemporal reconstruction while significantly reducing storage costs. Experimental results across multiple datasets show that our method achieves up to 10× higher compression ratios than rule-based state-of-the-art compressors such as SZ3, and up to 63% better performance than leading learning-based methods under the same reconstruction error.