Official Review · ICLR 2024

The paper considers a generalisation of the Schrödinger Bridge problem: initial and final marginals of the process are not probability measures. The authors derive that the time-reversal of diffusions with killing terms and show they correspond to diffusions with birth, and vice versa. Based on this result the authors updated the IPF algorithm and demonstrated its performance using biomedical data. - The considered problem statement is important as it naturally generalises the Diusion Schrodinger Bridge problem - The authors derived some fundamental result about the time-reversal of diffusions with killing terms - The experimental results are not very convincing. Even taking std into account still differences between results (for Ours and Ours - no death/births) are not that big. Is this difference really important for a considered downstream task? Ok, MMD is slightly smaller, and so what? Can we really better predict, e.g., responses to cancer drugs in practice? - Moreover, the dimensionality of considered data is rather limited. Although, the authors consider an important applied problem, it is not clear whether the proposed method is efficient for more high-dimensional tasks - The authors do not discuss computational complexity and robustness of the method. How does capacity of NNs influence the results? - The theoretical derivations look OK, but the practical implementation is very difficult to understand, follow and reproduce. - I have some expertise in diffusion processes, but the text is difficult to follow for non-experts in diffusion processes. Some important propositions, used by the authors while proving their main results, can be provided for completeness in the appendix - The description of the algorithm and of its each step are difficult to follow in the appendix - In Sec. 5, page 6, the authors introduce a TD loss. Why is it needed? Can the algorithm work without it? Any ablation study on how this loss influences the final quality of the results?