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Direct Product Flow Matching: Decoupling Radial and Angular Dynamics for Few-Shot Adaptation

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Flow matching distillation · 0 citations (OpenAlex)

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Proposes direct product flow matching (DP-FM), a constant-warping Riemannian flow on a decoupled cylindrical manifold with hidden-state classifier-free guidance, to improve multi-step few-shot adaptation of CLIP.

Problem

Existing flow-matching methods for few-shot VLM adaptation (FMA, HFM) couple radial and angular dynamics via flat or hyperbolic geometry, causing non-uniform angular speed, discarded modality-confidence information, and context-agnostic unconditional flows.

Approach

Reformulate cross-modal alignment on a warped product manifold and choose a constant warping function so radial and angular geodesics evolve independently (slerp on the sphere plus linear radial interpolation), and add classifier-free guidance conditioned on the VLM's hidden states.

Key results

• Under 16-shot with CLIP-LoRA, DP-FM reaches 79.2% average on difficult datasets (+3.1 over CLIP-LoRA baseline) and 89.4% on easy datasets, versus PLOT++ at 74.1% and 88.7%.
• With CLIP-Adapter at 16-shot on difficult datasets, DP-FM gains +9.9 average over the baseline, versus +5.5 for FMA and +7.8 for HFM.
• Compared with WP-FM Euclidean/Hyperbolic under the same CLIP setup, DP-FM improves the 16-shot average over difficult datasets to 72.5% from 71.9%.

Surprising findings

• Adding radial and CFG components without the time-shift schedule lowers accuracy (70.0%) relative to the baseline (71.1%), attributed to increased optimization complexity.

Limitations

• Inference requires multi-step integration, unlike single-step PEFT methods.
• Gains over strongest baselines on easy datasets are modest (about +1 to +2 points).
• The theoretical truncation-error claim is derived for first-order exponential Euler and relies on non-degeneracy assumptions.

Experimental setup

Datasets: FGVC Aircraft EuroSAT DTD SUN397 Stanford Cars Oxford Pets UCF101 Flowers102 Caltech101 Food101 ImageNet

Benchmarks: FGVC Aircraft EuroSAT DTD SUN397 Stanford Cars Oxford Pets UCF101 Flowers102 Caltech101 Food101 ImageNet

Metrics: classification accuracy

Baselines: FMA HFM WP-FM (Euclidean) WP-FM (Hyperbolic) CLIP-LoRA CLIP-Adapter CoOp CoCoOp TIP-Adapter PLOT++ KgCoOp ProGrad

Builds on: flow matching Riemannian flow matching FMA HFM CLIP-LoRA CLIP-Adapter classifier-free guidance

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