Airin Akter Tania | Searcharxiv

arXiv2026

Difficulty-Calibrated Interpolation Paths for Conditional Flow Matching

Conditional Flow Matching trains generative models by regressing a network onto the velocity of a prescribed noise-to-data interpolation path. The interpolation schedule that shapes this path is known to affect convergence and sample quality, yet it is invariably fixed in advance, independent of both the data and the model. We show that the regression difficulty of Conditional Flow Matching varies systematically along the path, and we propose Difficulty-Calibrated Flow Matching, which derives the schedule from the model itself: a short pilot run with the linear path records the per-time loss, and the schedule is set to the quantile function of this difficulty profile, so the trajectory lingers where the velocity is hardest to learn. The method has a single hyperparameter, leaves the training objective and its gradient equivalence intact, composes with classifier-free guidance, and adds about two percent training overhead. In controlled experiments on CIFAR-10, MNIST, and Fashion-MNIST with an identical compact U-Net, the calibrated path attains the best FID on CIFAR-10 at full sampling budget and clearly outperforms all fixed schedules in the large-batch, few-update regime, precisely the setting where compute is scarcest.

cs.CV↗

arXiv2026

AutoLumNet: Monotone Optimal Transport for Single-Shot Exposure Correction

Single-shot exposure correction aims to map an arbitrarily degraded image---whether under-exposed, over-exposed, or a spatial mixture of both---to a well-exposed output from a single capture. We present AutoLumNet, a framework that decomposes this task into a global monotone tone curve and a bounded local residual, making the global component the locus of formal guarantees. The tone curve is parameterized as the normalized cumulative integral of a strictly positive density, ensuring strict monotonicity by construction rather than by penalty. We prove that this parameterization (i)~preserves the pairwise luminance ordering of all pixels and all spatial extrema unconditionally, and (ii)~is dense in the space of valid tone corrections, containing the one-dimensional optimal-transport map from the input to any target luminance distribution. A differentiable sorted-sample Wasserstein-2 objective drives the learned curve toward the OT optimum during training. Spatially varying effects that the global map provably cannot address---local shading, chrominance shifts, and clipped-region restoration---are handled by a bounded residual decoder with dual-branch convex fusion, for which we provide an explicit sufficient condition for local order preservation. Experiments on five benchmarks (MSEC, SICE, LCDP, LOL-v1, LOL-v2-real) show that AutoLumNet achieves state-of-the-art PSNR and SSIM across both under- and over-exposure regimes at 11.2\,ms per frame, and generalizes zero-shot to pure low-light benchmarks without retraining. To our knowledge, AutoLumNet is the first exposure-correction method to unite structural monotonicity, optimal-transport optimality, and bounded local adaptivity within a single trainable architecture. Code is available at https://github.com/kraihan/Autolumnet.

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