# Supervised Score-Based Modeling by Gradient Boosting

arXiv: https://arxiv.org/abs/2411.01159 · HTML: https://mlsanity.com/paper/2411.01159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 2 Nov 2024.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Likelihood Ratios for Out-of-Distribution Detection](https://mlsanity.com/paper/1906.02845/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [CARD: Classification and Regression Diffusion Models](https://mlsanity.com/paper/2206.07275/) (2022)
- [NGBoost: Natural Gradient Boosting for Probabilistic Prediction](https://mlsanity.com/paper/1910.03225/) (2019)
- [A Comparative Analysis of XGBoost](https://mlsanity.com/paper/1911.01914/) (2019)
- [Score-Based Generative Classifiers](https://mlsanity.com/paper/2110.00473/) (2021)
- [Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees](https://mlsanity.com/paper/2406.07658/) (2024)

## Built on by (most cited first, 1 of 1)

- [SecDiff: Diffusion-Aided Secure Deep Joint Source-Channel Coding Against Adversarial Attacks](https://mlsanity.com/paper/2511.01466/) (2025)

## Abstract (arXiv)

Score-based generative models can effectively learn the distribution of data by estimating the gradient of the distribution. Due to the multi-step denoising characteristic, researchers have recently considered combining score-based generative models with the gradient boosting algorithm, a multi-step supervised learning algorithm, to solve supervised learning tasks. However, existing generative model algorithms are often limited by the stochastic nature of the models and the long inference time, impacting prediction performances. Therefore, we propose a Supervised Score-based Model (SSM), which can be viewed as a gradient boosting algorithm combining score matching. We provide a theoretical analysis of learning and sampling for SSM to balance inference time and prediction accuracy. Via the ablation experiment in selected examples, we demonstrate the outstanding performances of the proposed techniques. Additionally, we compare our model with other probabilistic models, including Natural Gradient Boosting (NGboost), Classification and Regression Diffusion Models (CARD), Diffusion Boosted Trees (DBT), and non-probabilistic GBM models. The experimental results show that our model outperforms existing models in both accuracy and inference time.