Research map / Image generation / Fast diffusion sampling

Learning to Solve Generative ODEs Beyond the Linear Span

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Rectified flow straightening · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes SpanLift, a frozen-backbone neural solver that adds a learned spatial residual operator to scalar-coefficient multistep updates, escaping the velocity-buffer span and improving few-step sampling without extra model NFEs.

Problem

Few-step sampling from diffusion and flow ODEs: learned or analytic scalar-coefficient multistep solvers can only produce updates inside the span of buffered velocity evaluations, leaving an out-of-span error floor at low NFE.

Approach

Decompose the solver mismatch into an in-span part and an orthogonal out-of-span residual, then augment a fixed scalar-coefficient base solver with a lightweight FiLM-conditioned spatial CNN residual operator over the state and velocity buffer, trained end-to-end by endpoint teacher matching.

Key results

• With 3 NFE on CIFAR-10, SpanLift improves FID from 8.16 (DyWeight) to 5.69.
• With 3 NFE on ImageNet 64x64, SpanLift reaches FID 11.83 versus 17.37 for DyWeight.
• On SANA-0.6B at NFE=3, SpanLift achieves FID 14.40 versus 19.82 for DyWeight; the learned operator's out-of-span ratio stays above 84% across steps and base solvers.

Surprising findings

• The learned residual correction is predominantly out-of-span (above 84% of its norm orthogonal to the velocity buffer), supporting the span-limitation analysis.
• Relative correction magnitude is largest for weak bases such as Euler (about 801% of the projected base step), while DyWeight needs under about 23%.

Limitations

• Gains are reported under extreme low-NFE budgets; benefit at higher NFE is less shown in the main text.
• Endpoint teacher matching does not define unique per-step targets, and the local span analysis does not cover schedule or endpoint learning effects.

Experimental setup

Datasets: CIFAR-10 ImageNet FFHQ AFHQv2 MJHQ-30K SEVIR

Benchmarks: CIFAR-10 ImageNet 64x64 FFHQ 64x64 AFHQv2 64x64 MJHQ-25K SEVIR precipitation nowcasting

Metrics: FID ImageReward HSS LPIPS CSI CSI-4 CSI-16

Baselines: iPNDM DPM-Solver++(3M) UniPC(3M) AMED-Solver AMED-Plugin EPD-Solver EPD-Plugin LD3 DLMS S4S-Alt DyWeight DDIM

Builds on: DyWeight iPNDM DPM-Solver++ EDM DLMS

Closest papers by meaning

• Bespoke Solvers for Generative Flow Models (ICLR 2024 · similarity 0.91)
• Distilling ODE Solvers of Diffusion Models into Smaller Steps (CVPR 2024 · similarity 0.90)
• SADA: Stability-guided Adaptive Diffusion Acceleration (ICML 2025 · similarity 0.89)
• DiffusionPDE: Generative PDE-Solving under Partial Observation (NeurIPS 2024 · similarity 0.89)
• Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment (CVPR 2025 · similarity 0.88)
• Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow (ICLR 2025 · similarity 0.88)