Explain the benefit of deterministic evaluation for FFM

Derive a theoretical explanation for why evaluating fixed-point flow matching by starting ODE integration from the deterministic central point \(X_0=0\), rather than from a random prior draw, improves performance, particularly in high-dimensional tasks.

Background

During experiments, the authors observed that replacing the stochastic prior draw used during training with the fixed initial point X0=0X_0=0 during evaluation improved performance, especially on high-dimensional humanoid tasks.

The paper reports this empirical effect but does not provide a theoretical account of why removing sampling stochasticity should improve performance or under what conditions the effect occurs. The authors explicitly defer that analysis to future work.

References

While this observation is very interesting and worth a more detailed analysis, in particular from a theoretical point of view, we leave this analysis for future work and apply the deterministic evaluation throughout our experiments.

— Reinforcement Learning via Fixed-point Flow Matching  (2610.12848 - Blessing et al., 9 Oct 2026) in Appendix H, Section “Further experiments and design ablations,” paragraph “Deterministic evaluation”