FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems

• URL: http://arxiv.org/abs/2603.01591v1
• Date: Mon, 02 Mar 2026 08:17:26 GMT
• Title: FAST-DIPS: Adjoint-Free Analytic Steps and Hard-Constrained Likelihood Correction for Diffusion-Prior Inverse Problems
• Authors: Minwoo Kim, Seunghyeok Shin, Hongki Lim,
• Abstract summary: Training-free diffusion priors often rely on repeated derivatives or inner optimization/MCMC loops with conservative step sizes.<n>We propose a training-free solver that replaces these inner loops with a hard measurement-space feasibility constraint.<n>Experiments achieve competitive PSNR/SSIM/LPIPS with up to 19.5$times$ speedup, without hand-coded adjoints or inner MCMC.
• Score: 2.9506605740700107
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Training-free diffusion priors enable inverse-problem solvers without retraining, but for nonlinear forward operators data consistency often relies on repeated derivatives or inner optimization/MCMC loops with conservative step sizes, incurring many iterations and denoiser/score evaluations. We propose a training-free solver that replaces these inner loops with a hard measurement-space feasibility constraint (closed-form projection) and an analytic, model-optimal step size, enabling a small, fixed compute budget per noise level. Anchored at the denoiser prediction, the correction is approximated via an adjoint-free, ADMM-style splitting with projection and a few steepest-descent updates, using one VJP and either one JVP or a forward-difference probe, followed by backtracking and decoupled re-annealing. We prove local model optimality and descent under backtracking for the step-size rule, and derive an explicit KL bound for mode-substitution re-annealing under a local Gaussian conditional surrogate. We also develop a latent variant and a one-parameter pixel$\rightarrow$latent hybrid schedule. Experiments achieve competitive PSNR/SSIM/LPIPS with up to 19.5$\times$ speedup, without hand-coded adjoints or inner MCMC.

Related papers

• RanSOM: Second-Order Momentum with Randomized Scaling for Constrained and Unconstrained Optimization [1.3537117504260623]
  Momentum methods, such as Polyak's Heavy Ball, are the standard for training deep networks but suffer from curvature-induced bias in settings.<n>We propose textbfRanSOM, a unified framework that eliminates this bias by replacing deterministic step sizes with randomized steps drawn from distributions with mean $_t$.<n>We instantiate this framework in two algorithms: textbfRanSOM-E for unconstrained optimization and textbfRanSOM-B for constrained optimization.
  arXiv  Detail & Related papers  (2026-02-06T16:09:36Z)
• Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs [56.246783503873225]
  This paper revisits the weighted strategy for non-stationary parametric bandits.<n>We propose a simpler weight-based algorithm that is as efficient as window/restart-based algorithms.<n>Our framework can be used to improve regret bounds of other parametric bandits.
  arXiv  Detail & Related papers  (2026-01-03T04:50:21Z)
• Residual subspace evolution strategies for nonlinear inverse problems [1.14219428942199]
  inverse problems pervade engineering and science, yet noisy, non-differentiable, or expensive residual evaluations routinely defeat Jacobian-based solvers.<n>This paper introduces residual subspace evolution strategies (RSES), a derivative-free solver that draws Gaussian probes around the current gradient, records how residuals change along those directions, and recombines the probes through a least-squares solve to produce an optimal update.
  arXiv  Detail & Related papers  (2025-12-11T06:20:13Z)
• Stochastic gradient descent for streaming linear and rectified linear systems with adversarial corruptions [8.756480554457985]
  We show novel nearly linear convergence guarantees of SGD-exp to the true parameter with up to $50%$ Massart corruption rate.<n>This is the first convergence guarantee result for robust ReLU regression in the streaming setting.
  arXiv  Detail & Related papers  (2024-03-02T12:45:01Z)
• An Efficient Rehearsal Scheme for Catastrophic Forgetting Mitigation during Multi-stage Fine-tuning [55.467047686093025]
  A common approach to alleviate such forgetting is to rehearse samples from prior tasks during fine-tuning.<n>We propose a sampling scheme, textttbf mix-cd, that prioritizes rehearsal of collateral damage'' samples.<n>Our approach is computationally efficient, easy to implement, and outperforms several leading continual learning methods in compute-constrained settings.
  arXiv  Detail & Related papers  (2024-02-12T22:32:12Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Smoothing ADMM for Sparse-Penalized Quantile Regression with Non-Convex Penalties [8.294148737585543]
  This paper investigates concave and clipped quantile regression in the presence of nonsecondary absolute and non-smooth convergence penalties. We introduce a novel-loop ADM algorithm with an increasing penalty multiplier, named SIAD, specifically for sparse regression.
  arXiv  Detail & Related papers  (2023-09-04T21:48:51Z)
• Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency [90.40062452292091]
  We present the first computationally efficient algorithm for linear bandits with heteroscedastic noise. Our algorithm is adaptive to the unknown variance of noise and achieves an $tildeO(d sqrtsum_k = 1K sigma_k2 + d)$ regret. We also propose a variance-adaptive algorithm for linear mixture Markov decision processes (MDPs) in reinforcement learning.
  arXiv  Detail & Related papers  (2023-02-21T00:17:24Z)
• Training \beta-VAE by Aggregating a Learned Gaussian Posterior with a Decoupled Decoder [0.553073476964056]
  Current practices in VAE training often result in a trade-off between the reconstruction fidelity and the continuity$/$disentanglement of the latent space. We present intuitions and a careful analysis of the antagonistic mechanism of the two losses, and propose a simple yet effective two-stage method for training a VAE. We evaluate the method using a medical dataset intended for 3D skull reconstruction and shape completion, and the results indicate promising generative capabilities of the VAE trained using the proposed method.
  arXiv  Detail & Related papers  (2022-09-29T13:49:57Z)
• On the Convergence of Stochastic Extragradient for Bilinear Games with Restarted Iteration Averaging [96.13485146617322]
  We present an analysis of the ExtraGradient (SEG) method with constant step size, and present variations of the method that yield favorable convergence. We prove that when augmented with averaging, SEG provably converges to the Nash equilibrium, and such a rate is provably accelerated by incorporating a scheduled restarting procedure.
  arXiv  Detail & Related papers  (2021-06-30T17:51:36Z)
• Balancing Rates and Variance via Adaptive Batch-Size for Stochastic Optimization Problems [120.21685755278509]
  In this work, we seek to balance the fact that attenuating step-size is required for exact convergence with the fact that constant step-size learns faster in time up to an error. Rather than fixing the minibatch the step-size at the outset, we propose to allow parameters to evolve adaptively.
  arXiv  Detail & Related papers  (2020-07-02T16:02:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.