# Sparse Scheduled Diffusion Guidance for Inverse Problems

arXiv: https://arxiv.org/abs/2603.07860 · HTML: https://mlsanity.com/paper/2603.07860/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Inverse problems and image restoration, one of 14 directions in Diffusion models.
- First posted on arXiv 9 Mar 2026.

## Placed in

- Diffusion models / [Inverse problems and image restoration](https://mlsanity.com/diffusion/inverse-problems-and-image-restoration/)

## Built on by (most cited first, 2 of 2)

- [Consistency Regularised Gradient Flows for Inverse Problems](https://mlsanity.com/paper/2605.07907/) (2026)
- [Perturb-and-Solve: Efficient Learned-Operator Conditioning for Latent Diffusion Inverse Problems](https://mlsanity.com/paper/2609.33171/) (2026)

## Abstract (arXiv)

Pretrained diffusion models are effective priors for Bayesian inverse problems, but posterior sampling with these priors is often costly because data-consistency guidance is applied throughout the full reverse trajectory. Existing methods have shown that vector-Jacobian products through the denoiser can sometimes be avoided, yet they typically still rely on dense guidance through the full trajectory or expensive inner solves. We introduce Sparse Scheduled Diffusion Guidance for Inverse Problems (Spin), a solver that avoids starting posterior sampling from pure noise. Spin first samples from a posterior time-marginal at an intermediate timestep t_*, and then uses that state as a warm start for a guided reverse diffusion process. At guidance time, instead of enforcing the measurement constraint at every denoising step, Spin applies lightweight corrections only at scheduled timesteps where the denoiser can still clean up artifacts. The resulting procedure decouples prior refinement from data consistency: the prior supplies denoising, while lightweight pixel-space optimization enforces the measurement constraint without backpropagation through the denoiser or decoder. Across linear and nonlinear inverse problems on FFHQ and ImageNet, Spin achieves competitive reconstruction quality with a substantially better runtime--memory profile, running 2x faster on pixel-space models and up to 50x faster on latent diffusion models, with lower memory costs.