# Backpropagation-Free Test-Time Adaptation via Probabilistic Gaussian Alignment

arXiv: https://arxiv.org/abs/2508.15568 · HTML: https://mlsanity.com/paper/2508.15568/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 73 references that are in the map.
- First posted on arXiv 21 Aug 2025.

## Builds on (most cited first, 30 of 46)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [BLIP: Bootstrapping Language-Image Pre-training for Unified Vision-Language Understanding and Generation](https://mlsanity.com/paper/2201.12086/) (2022)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Align before Fuse: Vision and Language Representation Learning with Momentum Distillation](https://mlsanity.com/paper/2107.07651/) (2021)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [CLIP-Adapter: Better Vision-Language Models with Feature Adapters](https://mlsanity.com/paper/2110.04544/) (2021)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Test-Time Prompt Tuning for Zero-Shot Generalization in Vision-Language Models](https://mlsanity.com/paper/2209.07511/) (2022)
- [Tip-Adapter: Training-free Adaption of CLIP for Few-shot Classification](https://mlsanity.com/paper/2207.09519/) (2022)
- [Learning to Propagate Labels: Transductive Propagation Network for Few-shot Learning](https://mlsanity.com/paper/1805.10002/) (2018)
- [Diverse Data Augmentation with Diffusions for Effective Test-time Prompt Tuning](https://mlsanity.com/paper/2308.06038/) (2023)
- [Efficient Test-Time Adaptation of Vision-Language Models](https://mlsanity.com/paper/2403.18293/) (2024)
- [Task Residual for Tuning Vision-Language Models](https://mlsanity.com/paper/2211.10277/) (2022)
- [SuS-X: Training-Free Name-Only Transfer of Vision-Language Models](https://mlsanity.com/paper/2211.16198/) (2022)
- [Align Your Prompts: Test-Time Prompting with Distribution Alignment for Zero-Shot Generalization](https://mlsanity.com/paper/2311.01459/) (2023)
- [Laplacian Regularized Few-Shot Learning](https://mlsanity.com/paper/2006.15486/) (2020)
- [Not All Features Matter: Enhancing Few-shot CLIP with Adaptive Prior Refinement](https://mlsanity.com/paper/2304.01195/) (2023)
- [C-TPT: Calibrated Test-Time Prompt Tuning for Vision-Language Models via Text Feature Dispersion](https://mlsanity.com/paper/2403.14119/) (2024)
- [On the test-time zero-shot generalization of vision-language models: Do we really need prompt learning?](https://mlsanity.com/paper/2405.02266/) (2024)
- [A Hard-to-Beat Baseline for Training-free CLIP-based Adaptation](https://mlsanity.com/paper/2402.04087/) (2024)
- [Dual Memory Networks: A Versatile Adaptation Approach for Vision-Language Models](https://mlsanity.com/paper/2403.17589/) (2024)
- [Dual Prototype Evolving for Test-Time Generalization of Vision-Language Models](https://mlsanity.com/paper/2410.12790/) (2024)
- [Boosting Vision-Language Models with Transduction](https://mlsanity.com/paper/2406.01837/) (2024)
- [DPCore: Dynamic Prompt Coreset for Continual Test-Time Adaptation](https://mlsanity.com/paper/2406.10737/) (2024)
- [Just Shift It: Test-Time Prototype Shifting for Zero-Shot Generalization with Vision-Language Models](https://mlsanity.com/paper/2403.12952/) (2024)

## Built on by (most cited first, 6 of 6)

- [ZOO-Prune: Training-Free Token Pruning via Zeroth-Order Gradient Estimation in Vision-Language Models](https://mlsanity.com/paper/2509.24837/) (2025)
- [Adapting Point Cloud Analysis via Multimodal Bayesian Distribution Learning](https://mlsanity.com/paper/2603.22070/) (2026)
- [Multi-modal Test-time Adaptation via Adaptive Probabilistic Gaussian Calibration](https://mlsanity.com/paper/2604.19093/) (2026)
- [[CLS] is Not Enough: Multi-Label Recognition via Patch-Level Inference and Adaptive Aggregation](https://mlsanity.com/paper/2605.25821/) (2026)
- [Von Mises-Fisher Mixture Model with Dynamic Shrinkage for Realistic Test-Time Transduction](https://mlsanity.com/paper/2607.15851/) (2026)
- [Not Every Correction Helps: Gain-Guided Continual Test-Time Adaptation](https://mlsanity.com/paper/2609.36655/) (2026)

## Abstract (arXiv)

Test-time adaptation (TTA) enhances the zero-shot robustness under distribution shifts by leveraging unlabeled test data during inference. Despite notable advances, several challenges still limit its broader applicability. First, most methods rely on backpropagation or iterative optimization, which limits scalability and hinders real-time deployment. Second, they lack explicit modeling of class-conditional feature distributions. This modeling is crucial for producing reliable decision boundaries and calibrated predictions, but it remains underexplored due to the lack of both source data and supervision at test time. In this paper, we propose ADAPT, an Advanced Distribution-Aware and backPropagation-free Test-time adaptation method. We reframe TTA as a Gaussian probabilistic inference task by modeling class-conditional likelihoods using gradually updated class means and a shared covariance matrix. This enables closed-form, training-free inference. To correct potential likelihood bias, we introduce lightweight regularization guided by CLIP priors and a historical knowledge bank. ADAPT requires no source data, no gradient updates, and no full access to target data, supporting both online and transductive settings. Extensive experiments across diverse benchmarks demonstrate that our method achieves state-of-the-art performance under a wide range of distribution shifts with superior scalability and robustness.