# Comparing SGLD and a fixed-noise predictor-corrector adaptation in canonical joint energy-based models on CIFAR-10

arXiv: https://arxiv.org/abs/2608.05025 · HTML: https://mlsanity.com/paper/2608.05025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 16 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Do Deep Generative Models Know What They Don't Know?](https://mlsanity.com/paper/1810.09136/) (2018)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Classifier-Free Guidance is a Predictor-Corrector](https://mlsanity.com/paper/2408.09000/) (2024)
- [Composition and Control with Distilled Energy Diffusion Models and Sequential Monte Carlo](https://mlsanity.com/paper/2502.12786/) (2025)
- [Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood](https://mlsanity.com/paper/2309.05153/) (2023)
- [EGC: Image Generation and Classification via a Diffusion Energy-Based Model](https://mlsanity.com/paper/2304.02012/) (2023)
- [Towards Bridging the Performance Gaps of Joint Energy-based Models](https://mlsanity.com/paper/2209.07959/) (2022)
- [Diffusion for Out-of-Distribution Detection on Road Scenes and Beyond](https://mlsanity.com/paper/2407.15739/) (2024)
- [Improving Adversarial Energy-Based Model via Diffusion Process](https://mlsanity.com/paper/2403.01666/) (2024)
- [Your Classifier Can Do More: Towards Balancing the Gaps in Classification, Robustness, and Generation](https://mlsanity.com/paper/2505.19459/) (2025)
- [Scalable Energy-Based Models via Adversarial Training: Unifying Discrimination and Generation](https://mlsanity.com/paper/2510.13872/) (2025)

## Abstract (arXiv)

Joint Energy-Based Models (JEM) unify classification and generation within a single network and support out-of-distribution (OOD) detection. Canonical JEM training relies on stochastic gradient Langevin dynamics (SGLD); a theoretically motivated alternative, the Predictor-Corrector (PC) sampler, has not previously undergone a systematic replication test on the canonical model. We reproduce canonical JEM on WideResNet-28-10 without normalisation layers on two independent runs and test a fixed-noise PC adaptation - with the degenerate annealed-noise predictor replaced by a deterministic gradient step - across three protocols: the adapted sampler replacing SGLD throughout the full training trajectories (115-132 epochs); cold-start generation (FID); and refinement-style multi-OOD detection (AUROC). The reconstruction reaches 92.88% test accuracy and buffer-FID 44.46 (canonical: 92.90% and 38.40). We document two failure modes: catastrophic late-training divergence with the signature of the canonical outlier-buffer mechanism (all four runs), and run-dependent SVHN OOD-discrimination dynamics. No consistent method-level advantage of the adaptation over SGLD is observed on any protocol: refinement AUROC differences stay below 0.007 across ten checkpoint-OOD pairs; seeded cold-start generation favours SGLD by about five FID points; on the training protocol a hierarchical seed-by-image bootstrap gives a 95% confidence interval on the macro-averaged AUROC difference that contains zero, while a seed-level equivalence test with two runs per method cannot establish formal equivalence. The training-protocol data are consistent both with equivalence and with a small directional effect. This outcome is consistent with theory: the guarantees of the annealed-noise PC framework do not transfer to the constant-noise regime of canonical JEM.