Empirical evaluation demonstrates low-step generative gains via target-speed reweighting in image models, indicating that mathematical refinement diverges from sample quality.
Key Points
Investigate why generative flow quality does not improve monotonically with finer numerical integration in Product Manifold Flow Matching and identify the mechanisms driving low-step performance.
Trained 32 M and 129 M parameter flow-matching models on CIFAR-100 and a synthetic pile-driver dataset using products of hyperbolic factor spaces with exponential-map Euler updates.
Evaluated generative fidelity across varying numbers of function evaluations (NFEs) against standard Euclidean baselines across multiple architecture-seed configurations.
Conducted factor-wise ablation studies isolating the influence of geometric curvature from target-speed reweighting mechanisms.
Product models at NFE = 4 achieved lower FID than Euclidean baselines at NFE = 32 across all six architecture-seed configurations, reducing sampling time by approximately eightfold.
Applying factor-wise target-speed reweighting to Euclidean baselines replicated the low-NFE advantage across three seeds, whereas omitting it from Product models degraded FID at NFE ≥ 4.
FID reached optimal scores at NFE = 8 on CIFAR-100 and NFE = 4 on the synthetic dataset, despite continuous decreases in numerical integration errors at higher step counts.