Abstract
While diffusion models have revolutionized image synthesis, their application to real-world inverse problems is often hampered by the need for massive datasets and the difficulty of imposing strict physical constraints. In this work, we introduce \textbf{SE-UNet} (Singular Equivariant UNet), a framework designed to solve ill-posed imaging tasks without extensive pre-training. By treating generation as an optimization problem constrained by geometric equivariance (D4 group) and singular value gating, SE-UNet effectively standardizes the solution space. We demonstrate that these strong inductive biases allow for state-of-the-art zero-shot inpainting results (80% missing pixels) on CIFAR-10. Our method surpasses Deep Image Prior (DIP) baselines by over 4 dB in PSNR and exhibits a characteristic "singular snap" convergence -- rapidly locking into the signal manifold. SE-UNet thus offers a data-efficient pathway for constrained generation, aligning with the ReALM-GEN goal of bridging theoretical priors with practical deployment.
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May 30, 2026cs.CV
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Oct 2, 2025eess.IV
Diffusion models have emerged as powerful generative priors for solving inverse imaging problems. However, their practical deployment is hindered by the substantial computational cost of slow, multi-step sampling. Although Consistency Models (CMs) address this limitation by enabling high-quality generation in only one or a few steps, their direct application to inverse problems has remained largely unexplored. This paper introduces a modified consistency sampling framework specifically designed for inverse problems. The proposed approach regulates the sampler's stochasticity through a measurement-consistency mechanism that leverages the degradation operator, thereby enforcing fidelity to the observed data while preserving the computational efficiency of consistency-based generation. Comprehensive experiments on the Fashion-MNIST and LSUN Bedroom datasets demonstrate consistent improvements across both perceptual and pixel-level metrics, including the Fréchet Inception Distance (FID), Kernel Inception Distance (KID), peak signal-to-noise ratio (PSNR), and structural similarity index measure (SSIM), compared with baseline consistency and diffusion-based sampling methods. The proposed method achieves competitive or superior reconstruction quality with only a small number of sampling steps.
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Pretrained diffusion models have revolutionized real-world image super-resolution (Real-ISR) but suffer from computational bottlenecks due to iterative sampling. Recent single-step distillation accelerates inference but faces a stark perception-distortion trade-off due to rigid timestep initialization, distributional trajectory mismatches, and fragile stochastic modulation. To address this, we present Adaptive Inversion and Degradation-aware Sampling for Real-ISR (IDaS-SR), a one-step framework bridging the deterministic restoration and stochastic generation manifolds. At its core, the Manifold Inversion Noise Estimator (MINE) resolves these initialization and trajectory mismatches by predicting a severity-aware timestep and inversion noise, precisely anchoring low-quality latents onto the diffusion trajectory. Furthermore, to mitigate fragile stochastic modulation, we propose CHARIOT, a continuous generative steering mechanism. By rescheduling trajectories and interpolating noise, it enables explicit navigation of the perception-distortion boundary without compromising structural priors. Extensive experiments demonstrate that IDaS-SR outperforms state-of-the-art methods, seamlessly transitioning from a rigorous structural restorer to a sophisticated texture hallucinator in a single inference step.
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