Generative Learning for Slow Manifolds and Bifurcation Diagrams

The paper proposes an applied framework (Algorithm 1) for conditional sampling on slow/bifurcation manifolds using cSGMs and optional Geometric Harmonics lifting, and demonstrates it empirically on cusp and PDE examples, but it does not state or prove a quantitative convergence guarantee. It explicitly notes mismatches (e.g., non-uniform sampling slices where the learned conditional is “not an exact match”) and leaves exact distributional matching as future work, indicating the absence of a formal error analysis . By contrast, the candidate solution supplies a standard SDE-based W1 error decomposition (score error via synchronous coupling + Grönwall, Euler–Maruyama strong error, and a GH lifting approximation term), which is logically correct under its stated regularity and approximation assumptions. Hence the paper is incomplete on theory, while the model’s proof is correct as a conditional result.