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

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
inverse problemimage reconstructiondiffusion models
Abstract:

FAST-DIPS\textbf{FAST-DIPS} is a training-free solver for diffusion-prior inverse problems, including nonlinear forward operators. At each noise level, a pretrained denoiser provides an anchor x0∣t\mathbf{x}_ {0|t}; we then perform a hard-constrained proximal correction in measurement space (AWGN) by solving min⁡x12γt∥x−x0∣t∥2 s.t. ∥A(x)−y∥≤ε\min_\mathbf{x} \tfrac{1}{2\gamma_t}\|\mathbf{x}-\mathbf{x}_{0|t}\|^2 \ \text{s.t.}\ \|\mathcal{A}(\mathbf{x})-\mathbf{y}\|\le\varepsilon. The correction is implemented via an adjoint-free ADMM with a closed-form projection onto the Euclidean ball and a few steepest-descent updates whose step size is analytic and computable from one VJP and one JVP—or a forward-difference surrogate—followed by decoupled re-annealing. We show this step minimizes a local quadratic model (with backtracking-based descent), any ADMM fixed point satisfies KKT for the hard-constraint, and mode substitution yields a bounded time-marginal error. We also derive a latent variant A↦A∘D\mathcal{A}\mapsto\mathcal{A}\circ\mathcal{D} and a one-parameter pixel→\rightarrowlatent hybrid schedule. FAST-DIPS delivers comparable or better PSNR/SSIM/LPIPS while being substantially faster, requiring only autodiff access to A\mathcal{A} and no hand-coded adjoints or inner MCMC.

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Overview

Overall Novelty Assessment

FAST-DIPS introduces a training-free solver for diffusion-prior inverse problems that combines hard-constrained proximal correction with adjoint-free ADMM optimization. The paper resides in the 'Acceleration and Efficiency Improvements' leaf under 'Training-Free and Plug-and-Play Approaches,' alongside only two sibling papers. This sparse leaf structure suggests the specific combination of acceleration techniques and hard-constraint enforcement represents a relatively focused research direction within the broader training-free landscape, which itself contains multiple complementary methodological clusters addressing posterior sampling, latent representations, and domain-specific applications.

The taxonomy reveals that FAST-DIPS sits within a larger ecosystem of training-free methods, neighboring 'Plug-and-Play Diffusion Frameworks' that emphasize measurement consistency without test-time adaptation. The parent branch excludes methods requiring task-specific training, distinguishing it from 'Training and Adaptation Methods' that employ fine-tuning or distillation. Nearby branches include 'Core Algorithmic Frameworks' focused on posterior approximation theory and 'Latent Space Methods' operating in compressed domains. The scope notes clarify that acceleration methods like FAST-DIPS differ from amortized inference approaches by maintaining iterative sampling while reducing computational cost through algorithmic innovations rather than model distillation.

Among thirty candidates examined across three contributions, none yielded clear refutations. The 'FAST-DIPS framework with adjoint-free analytic steps' examined ten candidates with zero refutable matches, as did the 'hard-constrained likelihood correction mechanism' and 'adjoint-free analytic step computation' contributions. This absence of overlapping prior work within the limited search scope suggests the specific technical combination—hard constraints via ADMM with closed-form projections and analytic step sizes from VJP/JVP operations—may represent a novel synthesis. However, the search examined only top-thirty semantic matches, leaving open whether broader literature contains related constraint-handling or adjoint-free optimization strategies in diffusion contexts.

Based on the limited search scope, FAST-DIPS appears to occupy a distinct position combining hard-constraint enforcement with computational efficiency mechanisms not directly matched in the examined candidates. The sparse leaf structure and absence of refutations across thirty candidates suggest novelty in the specific technical approach, though the analysis cannot rule out related work beyond the top-K semantic neighborhood or in adjacent optimization literature outside the diffusion-prior inverse problem framing.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
0
Refutable Paper

Research Landscape Overview

Core task: Solving inverse problems with diffusion priors. The field has organized itself around several complementary research directions. Core Algorithmic Frameworks and Posterior Sampling Methods develop foundational techniques for approximating Bayesian posteriors using pretrained diffusion models, often building on score-based or Tweedie-style updates. Latent Space and Compressed Representation Methods exploit lower-dimensional embeddings to improve efficiency, while Blind and Adaptive Inverse Problems tackle scenarios where forward operators or noise levels are unknown. Training-Free and Plug-and-Play Approaches emphasize using off-the-shelf diffusion priors without retraining, contrasting with Training and Adaptation Methods that fine-tune models for specific tasks. Domain-Specific Applications and Modalities span medical imaging, audio reconstruction, and scientific data, and Theoretical Analysis and Benchmarking provide rigorous guarantees and standardized evaluation. Representative works include Hard Data Consistency[3] and Pseudoinverse-guided Diffusion[8] in training-free settings, Posterior Sampling Latent[11] in compressed domains, and Survey Diffusion Inverse[15] offering a broad overview. Within the training-free landscape, a particularly active line of work focuses on acceleration and efficiency improvements, addressing the computational burden of iterative diffusion sampling. Methods such as Come-Closer-Diffuse-Faster[24] and Think Twice MCMC[45] explore strategies to reduce the number of function evaluations or sampling steps while maintaining solution quality. FAST-DIPS[0] sits squarely in this acceleration-focused cluster, proposing techniques to speed up diffusion-based inverse problem solvers without requiring model retraining. Compared to Hard Data Consistency[3], which enforces measurement constraints at each step, FAST-DIPS[0] emphasizes computational efficiency trade-offs. Meanwhile, Variational Perspective[5] offers a complementary theoretical lens on posterior approximation, highlighting the diversity of methodological angles even within training-free approaches. Open questions remain around balancing speed, accuracy, and the flexibility to handle diverse forward models across modalities.

Claimed Contributions

FAST-DIPS framework with adjoint-free analytic steps

The authors introduce FAST-DIPS, a new framework for diffusion-prior inverse problems that eliminates the need for adjoint computations through analytic steps while incorporating hard-constrained likelihood correction. This approach aims to simultaneously achieve high reconstruction quality and computational efficiency.

10 retrieved papers
Hard-constrained likelihood correction mechanism

The authors develop a likelihood correction mechanism that enforces hard constraints during the diffusion-based reconstruction process. This component works in conjunction with the adjoint-free analytic steps to improve solution quality.

10 retrieved papers
Adjoint-free analytic step computation

The authors propose a method to compute reconstruction steps analytically without requiring adjoint operations, which reduces computational overhead while maintaining reconstruction accuracy in diffusion-prior inverse problems.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

FAST-DIPS framework with adjoint-free analytic steps

The authors introduce FAST-DIPS, a new framework for diffusion-prior inverse problems that eliminates the need for adjoint computations through analytic steps while incorporating hard-constrained likelihood correction. This approach aims to simultaneously achieve high reconstruction quality and computational efficiency.

Contribution

Hard-constrained likelihood correction mechanism

The authors develop a likelihood correction mechanism that enforces hard constraints during the diffusion-based reconstruction process. This component works in conjunction with the adjoint-free analytic steps to improve solution quality.

Contribution

Adjoint-free analytic step computation

The authors propose a method to compute reconstruction steps analytically without requiring adjoint operations, which reduces computational overhead while maintaining reconstruction accuracy in diffusion-prior inverse problems.

Table of Contents