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Distance Marching for Generative Modeling

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Flow matching and flow sampling · 0 citations (OpenAlex)

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Proposes Distance Marching, a time-unconditional generative model that learns a distance-like scalar field plus a direction field with distance-focused losses (one-step and directional eikonal), enabling gradient descent or sphere-tracing sampling on CIFAR-10 and ImageNet.

Problem

Time-unconditional generative models suffer from target ambiguity: the same noisy input maps to multiple noise levels and conflicting denoising directions, and existing time-free methods are fragile or lower quality.

Approach

Learn a distance-like scalar field depending only on position, trained with a one-step loss that inverse-distance-weights closer data targets and a directional eikonal loss that fixes the offset; inference uses sphere tracing or gradient descent without time input.

Key results

• Distance Marching achieves FID 2.23 on unconditional CIFAR-10 with sphere tracing (tied best among time-unconditional methods), versus 3.34 for EM and 3.36 for EqM.
• On class-conditional ImageNet B/2, gradient descent reaches FID 32.16, beating SiT-B/2 standard FM (36.68) and Equilibrium Matching-B/2 (32.85) with 250 steps.
• Distance Marching reaches flow matching's final FID using under 60% of sampling steps, and adaptive GD cuts average steps by 29.7% (250 to 175.8).

Surprising findings

• Gradient descent with a non-curl-free direction field converges without enforcing the vector field to be a gradient of a scalar potential.
• A tiny distance predictor (about 0.1M parameters) achieves OOD AUROC avg 0.79, beating EqM (130M) on average.

Limitations

• Sphere tracing gives slightly worse final ImageNet FID than gradient descent at 250 steps.
• Sample diversity may be limited; MCMC refinement is left as future work.
• Gains on CIFAR-10 are tied with uEDM.

Experimental setup

Datasets: CIFAR-10 ImageNet-256

Benchmarks: CIFAR-10 ImageNet-256 SVHN Textures Constant

Metrics: FID sFID IS AUROC W2 Hausdorff distance Chamfer distance

Baselines: FM OT-CFM SB-CFM Energy Matching Equilibrium Matching uEDM SiT-B/2 DiT-B/2 EDM NCSN++ DDPM++ IGEBM

Builds on: flow matching SiT EDM sphere tracing Equilibrium Matching

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