2405.15020
AdjointDEIS: Efficient Gradients for Diffusion Models
Zander W. Blasingame, Chen Liu
correctmedium confidence
- Category
- Not specified
- Journal tier
- Strong Field
- Processed
- Sep 28, 2025, 12:56 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper proves that for Stratonovich SDEs with additive diffusion g(t) independent of the state, the adjoint ax(t) satisfies a backward deterministic ODE; it derives this via stochastic flows and a backward Stratonovich adjoint equation in which the ∂g/∂x term vanishes when g=g(t). The candidate solution reaches the same adjoint ODE by a pathwise variational/Jacobian-flow argument. The assumptions align, the terminal condition matches, and both explain why no stochastic term appears. The approaches are different but consistent.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} strong field
\textbf{Justification:}
The core theorem that the adjoint of a Stratonovich SDE with additive diffusion g(t) is governed by a deterministic ODE is both correct and practically meaningful. The paper's derivation via stochastic flows and a backward Stratonovich adjoint equation is rigorous, and the specialization to g=g(t) is handled cleanly. Minor clarifications on notation (row vs. column) and explicit restatement of assumptions/terminal conditions in the main theorem would enhance clarity.