# Fundamental Recovery Bounds for SPAD Signals under Stationary Flux

arXiv: https://arxiv.org/abs/2601.07599 · HTML: https://mlsanity.com/paper/2601.07599/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 50 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [A megapixel time-gated SPAD image sensor for 2D and 3D imaging applications](https://mlsanity.com/paper/1912.12910/) (2019)
- [Quanta Burst Photography](https://mlsanity.com/paper/2006.11840/) (2020)
- [High Flux Passive Imaging with Single-Photon Sensors](https://mlsanity.com/paper/1902.10190/) (2019)
- [Photon-Flooded Single-Photon 3D Cameras](https://mlsanity.com/paper/1903.08347/) (2019)
- [Passive Inter-Photon Imaging](https://mlsanity.com/paper/2104.00059/) (2021)
- [Motion Adaptive Deblurring with Single-Photon Cameras](https://mlsanity.com/paper/2012.07931/) (2020)
- [What Does a One-Bit Quanta Image Sensor Offer?](https://mlsanity.com/paper/2208.10350/) (2022)
- [Parallel Diffusion Model-based Sparse-view Cone-beam Breast CT](https://mlsanity.com/paper/2303.12861/) (2023)
- [Score-Based Diffusion Models for Photoacoustic Tomography Image Reconstruction](https://mlsanity.com/paper/2404.00471/) (2024)
- [Time-Resolved MNIST Dataset for Single-Photon Recognition](https://mlsanity.com/paper/2410.16744/) (2024)
- [Bayesian Cram'er-Rao Bound Estimation with Score-Based Models](https://mlsanity.com/paper/2309.16076/) (2023)

## Abstract (arXiv)

Single-photon avalanche diodes (SPADs) record light as a discrete stream of individual detections. The signal is stochastic. Its statistical structure depends on the sensor's operation mode: binary detection in fixed bins, timestamped detection in fixed bins, or free-running timestamped detection. We derive the likelihood score function for each of these three passive modes. From this single object, stem both fundamental limits of recovery (Cramer-Rao bounds) and practical recovery algorithms based on diffusion posterior sampling. The paper further generalizes fundamental limits to Bayesian Cramer-Rao lower bounds. This generalization makes use of a learned approximation of the score function of signal priors. In prior art, analyses and diffusion-based reconstruction for SPAD data have treated individual modes in isolation. Our unified treatment shows a qualitative high-flux gap between modes: binary counts saturate exponentially, while timestamped modes degrade only linearly. We further extend diffusion posterior sampling, previously restricted to binary SPAD data, to a full timestamped case using the suitable score function. We demonstrate experimentally that matching the score to the operation mode is beneficial for high-fidelity reconstruction. By tying the recovery bounds and diffusion to the score function, this work aims to establish a common foundation for both asking what is recoverable in single-photon sensing, and building methods that approach the bound.