# Trajectory Constraints for Imaging Inverse Problems

arXiv: https://arxiv.org/abs/2605.29012 · HTML: https://mlsanity.com/paper/2605.29012/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 13 of 13)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [SITCOM: Step-wise Triple-Consistent Diffusion Sampling for Inverse Problems](https://mlsanity.com/paper/2410.04479/) (2024)
- [Analysis of Deep Image Prior and Exploiting Self-Guidance for Image Reconstruction](https://mlsanity.com/paper/2402.04097/) (2024)
- [Measurement Score-Based Diffusion Model](https://mlsanity.com/paper/2505.11853/) (2025)
- [Self-diffusion for Solving Inverse Problems](https://mlsanity.com/paper/2510.21417/) (2025)
- [UGoDIT: Unsupervised Group Deep Image Prior Via Transferable Weights](https://mlsanity.com/paper/2505.11720/) (2025)
- [Sequential Diffusion-Guided Deep Image Prior For Medical Image Reconstruction](https://mlsanity.com/paper/2410.04482/) (2024)

## Abstract (arXiv)

Diffusion models have achieved strong performance in imaging inverse problems, but typically rely on domain-matched pretrained models and external training data. Moreover, errors introduced at intermediate reverse-sampling steps can accumulate and degrade the final reconstruction, with their propagation strongly influenced by how successive states are related. We propose TRACE, a training-free TRAjectory-Constrained rEconstruction framework for imaging inverse problems. TRACE replaces the pretrained diffusion model with an untrained overparameterized network optimized directly from the observed measurements and organizes reconstruction as a sequence of intermediate states. At each step, TRACE enforces stochastic proximal consistency (SPC) by inferring each reconstruction from a stochastically perturbed predecessor under measurement consistency, while proximally constraining the resulting estimate to its corresponding unperturbed state. This formulation admits a proximal interpretation, from which we derive stability bounds characterizing the variation between consecutive states under approximate network updates. A local Jacobian analysis further characterizes how SPC regularizes the network-parameterized reconstruction. Experiments on natural-image restoration and CT reconstruction demonstrate competitive performance against both untrained and pretrained neural-prior methods. We further show that the proposed trajectory constraint can be incorporated into existing diffusion-based inverse solvers to improve reconstruction performance.