2407.07873
Dynamical Measure Transport and Neural PDE Solvers for Sampling
Jingtong Sun, Julius Berner, Lorenz Richter, Marius Zeinhofer, Johannes Müller, Kamyar Azizzadenesheli, Anima Anandkumar
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper’s Proposition 3.1 and Appendix A.3 establish the three BSDE loss equivalences using the same identities the model employs: (i) a reparametrization µ̃=f+σu and σ⊤∇Ṽ=u+v, together with Tr(σσ⊤∇2V)=div(σσ⊤∇V); (ii) the Itô–Stratonovich conversion yielding the divergence correction; and (iii) the substitution u=σ⊤∇V. The candidate solution reproduces these steps cleanly (without relying on optimality/Nelson’s relation) and matches the paper’s algebra term-by-term, assuming σ is independent of x and sufficient regularity—assumptions also used in the paper.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The loss equivalences are correct and useful, and the PDE/BSDE framing cleanly unifies prior trajectory-based methods. The proof steps are standard and sufficiently rigorous under the stated smoothness and time-dependent diffusion assumptions. A few clarifications (notational consistency, explicit reminder that σ is independent of x, and that Nelson’s relation is not strictly required for the reparametrization step) would improve readability and avoid potential confusion.