# SDPM: Survival Diffusion Probabilistic Model for Continuous-Time Survival Analysis

arXiv: https://arxiv.org/abs/2605.22776 · HTML: https://mlsanity.com/paper/2605.22776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 21 of its 53 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 21 of 21)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Machine Learning for Survival Analysis: A Survey](https://mlsanity.com/paper/1708.04649/) (2017)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [Deep Recurrent Survival Analysis](https://mlsanity.com/paper/1809.02403/) (2018)
- [SurvTRACE: Transformers for Survival Analysis with Competing Events](https://mlsanity.com/paper/2110.00855/) (2021)
- [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018)
- [Unbiased split variable selection for random survival forests using maximally selected rank statistics](https://mlsanity.com/paper/1605.03391/) (2016)
- [High-Dimensional Survival Analysis: Methods and Applications](https://mlsanity.com/paper/2205.02948/) (2022)
- [An Introduction to Deep Survival Analysis Models for Predicting Time-to-Event Outcomes](https://mlsanity.com/paper/2410.01086/) (2024)
- [Hierarchical Transformer for Survival Prediction Using Multimodality Whole Slide Images and Genomics](https://mlsanity.com/paper/2211.16632/) (2022)
- [Deep Learning for Survival Outcomes](https://mlsanity.com/paper/1904.10345/) (2019)
- [SAVAE: Leveraging the variational Bayes autoencoder for survival analysis](https://mlsanity.com/paper/2312.14651/) (2023)
- [SurvDiff: A Diffusion Model for Generating Synthetic Data in Survival Analysis](https://mlsanity.com/paper/2509.22352/) (2025)

## Abstract (arXiv)

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, mathbbP(T,δ mid x), using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.