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Root-Selecting Fixed-Point Inversion for Rectified Flows via Trajectory Straightness

NeurIPS 2026 · Point clouds › Shape and surface completion · approach: Point cloud diffusion generation · 0 citations (OpenAlex)

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Proposes SelFix, a fixed-point inversion method for rectified flows that selects, among multiple approximate local inverse roots, the one inducing the straightest inverse trajectory, via an anchored Halpern iteration with decoupled momentum.

Problem

Fixed-point inversion of rectified flows can converge to distinct approximate roots of the local inverse equation with similar residuals but different reconstruction and editing quality; existing methods do not specify which root to pick.

Approach

Treat fixed-point inversion as root selection over the exact local inverse set, use a causal discretized trajectory-straightness proxy whose minimizer is the projection of a straightness anchor onto the fixed-point set, and reach it with a vanishing-anchor Halpern iteration plus decoupled momentum on the fixed-point term.

Key results

• On PIE-Bench reconstruction with FLUX.1-dev, SelFix reaches PSNR 28.29 and LPIPS 0.0742, versus 26.98 PSNR for FireFlow and 15.05 for naive FPI.
• SelFix reduces the accumulated straightness proxy from 0.1855 (FPI) to 0.1505 and DS from 0.2080 to 0.1702.
• SelFix achieves the lowest structure distance and best background-preservation scores in PIE-Bench editing, per the authors.

Surprising findings

• Naive fixed-point iteration (FPI) performs much worse than direct reverse integration (ReFlow) in reconstruction (PSNR 15.05 vs 19.54).

Limitations

• Convergence guarantee is local and asymptotic under nonexpansiveness and a nonempty local fixed-point set; practice uses finite inner iterations (at most 10).
• Results rely on a single backbone (FLUX.1-dev) and one benchmark (PIE-Bench).
• Multi-root claim is empirical and restricted to the learned discretized inverse equation.

Experimental setup

Datasets: PIE-Bench

Benchmarks: PIE-Bench

Metrics: LPIPS SSIM PSNR DS CLIP similarity structure distance background PSNR/LPIPS/SSIM

Baselines: ReFlow RF-Solver FireFlow ReNoise AIDI FPI

Builds on: Halpern iteration rectified flow ReNoise RF-Solver FireFlow

Closest papers by meaning

• FireFlow: Fast Inversion of Rectified Flow for Image Semantic Editing (ICML 2025 · similarity 0.86)
• Flow Priors for Linear Inverse Problems via Iterative Corrupted Trajectory Matching (NeurIPS 2024 · similarity 0.85)
• Taming Rectified Flow for Inversion and Editing (ICML 2025 · similarity 0.85)
• SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories (NeurIPS 2025 · similarity 0.84)
• Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations (ICLR 2025 · similarity 0.84)
• Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solving (NeurIPS 2025 · similarity 0.84)