Ashesh Chattopadhyay

10/10 🚀 Closing Our framework links spectral physics + SDE theory to define when diffusion models succeed—or fail—on multi-scale systems. This theory provides a blueprint for stable, high-fidelity generative modeling of physical dynamics.

9/10 📌 Key Theoretical Insights ⚡ Spectral collapse is SDE-driven ⚡ Linear schedules are incompatible with power-law systems ⚡ β(τ) must be designed as a spectral operator ⚡ One-step generators emerge naturally from score geometry

🧵 1/10 We introduce a new theoretical framework for continuous score-based diffusion models, showing that standard DDPMs contain a built-in spectral failure mode when applied to any multiscale, power-law physical system. arxiv.org/abs/2512.09572

📄 Paper: Lupin-Jimenez et al. (2025) "Simultaneous Emulation and Downscaling..." doi.org/10.1029/2025JH… 💾 Code & data: zenodo.org/record/14607130 We’d love to hear from collaborators in ocean ML, emulation, and climate AI 🌊🤝

🚀 Why it’s exciting: ✅ Physically grounded ✅ 10x–1000x faster than ROMS ✅ Enables regional “digital twins” ✅ Sets up for coupled ocean–atmosphere emulation ✅ Works across different reanalysis sources AI meets ocean science.

🚨 New from our group! A stable AI framework for high-res regional ocean modeling-- joint work with Fujitsu Research and NC State led by @ucsc PhD students Lenny and @MoeinDarman . Now out in JGR: Machine Learning & Computation 🌊🤖 🔗 doi.org/10.1029/2025JH… 🧵

Led by @ucsc PhD students Niloofar & Lenny with Tianning Wu & Roy He from @NCState (5/5)

Our method is: ⚡️ One-shot 🌀 Physically-consistent 🌐 Scalable It captures high-wavenumber, fine-scale structures other ML baselines miss. Spectral diagnostics & vorticity metrics confirm this. (4/5)

🚨 New preprint alert! “Generative Lagrangian Data Assimilation for Ocean Dynamics Under Extreme Sparsity” is live! 📄 arxiv.org/abs/2507.06479🌊 Reconstructs high-res ocean states from just 0.1% data using #GenAI. No forward model needed. (1/5)