2503.00718
Differentiating Unstable Diffusion
Angxiu Ni
incompletemedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Theorem 1 states exactly the path‑kernel formula, but the authors explicitly note that the discrete‑time derivation is rigorous while the passage to continuous time and long time is only formal (“without rigorous proof”) and assumes interchange of limits/integrals . By contrast, the candidate solution supplies a standard continuous‑time proof under explicit regularity hypotheses (stochastic flow differentiability, Jacobian flow, martingale representation), and it reproduces the same formula as Theorem 1 in the paper . Hence the model is correct and complete under stated assumptions, while the paper’s main continuous‑time argument remains incomplete.
Referee report (LaTeX)
\textbf{Recommendation:} major revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The paper introduces a useful and conceptually clear path–kernel linear-response framework that interpolates between established approaches and offers practical guidance for unstable systems. However, the main continuous-time theorem and ergodic extensions are presented as formal limits without rigorous justification. Elevating these to fully rigorous statements under explicit assumptions (as demonstrated in the model solution) would materially improve correctness and reproducibility.