# Distribution Shift Inversion for Out-of-Distribution Prediction

arXiv: https://arxiv.org/abs/2306.08328 · HTML: https://mlsanity.com/paper/2306.08328/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 82 of its 91 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Builds on (most cited first, 30 of 82)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [CyCADA: Cycle-Consistent Adversarial Domain Adaptation](https://mlsanity.com/paper/1711.03213/) (2017)
- [In Search of Lost Domain Generalization](https://mlsanity.com/paper/2007.01434/) (2020)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Learning Robust Global Representations by Penalizing Local Predictive Power](https://mlsanity.com/paper/1905.13549/) (2019)
- [Deeper, Broader and Artier Domain Generalization](https://mlsanity.com/paper/1710.03077/) (2017)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)

## Built on by (most cited first, 23 of 23)

- [Learning-to-Cache: Accelerating Diffusion Transformer via Layer Caching](https://mlsanity.com/paper/2406.01733/) (2024)
- [Diffusion Model as Representation Learner](https://mlsanity.com/paper/2308.10916/) (2023)
- [Priority-Centric Human Motion Generation in Discrete Latent Space](https://mlsanity.com/paper/2308.14480/) (2023)
- [Tackling Structural Hallucination in Image Translation with Local Diffusion](https://mlsanity.com/paper/2404.05980/) (2024)
- [GDA: Generalized Diffusion for Robust Test-time Adaptation](https://mlsanity.com/paper/2404.00095/) (2024)
- [FOOGD: Federated Collaboration for Both Out-of-distribution Generalization and Detection](https://mlsanity.com/paper/2410.11397/) (2024)
- [Tackling Hallucination from Conditional Models for Medical Image Reconstruction with DynamicDPS](https://mlsanity.com/paper/2503.01075/) (2025)
- [Adversarially Robust Out-of-Distribution Detection Using Lyapunov-Stabilized Embeddings](https://mlsanity.com/paper/2410.10744/) (2024)
- [StyDeSty: Min-Max Stylization and Destylization for Single Domain Generalization](https://mlsanity.com/paper/2406.00275/) (2024)
- [FDS: Feedback-guided Domain Synthesis with Multi-Source Conditional Diffusion Models for Domain Generalization](https://mlsanity.com/paper/2407.03588/) (2024)
- [Generator Born from Classifier](https://mlsanity.com/paper/2312.02470/) (2023)
- [Watch the Watcher! Backdoor Attacks on Security-Enhancing Diffusion Models](https://mlsanity.com/paper/2406.09669/) (2024)
- [Dual-Path Adversarial Lifting for Domain Shift Correction in Online Test-time Adaptation](https://mlsanity.com/paper/2408.13983/) (2024)
- [Distribution Shift Aware Neural Tabular Learning](https://mlsanity.com/paper/2508.19486/) (2025)
- [What's in a Latent? Leveraging Diffusion Latent Space for Domain Generalization](https://mlsanity.com/paper/2503.06698/) (2025)
- [Diagnosing and Rectifying Fake OOD Invariance: A Restructured Causal Approach](https://mlsanity.com/paper/2312.09758/) (2023)
- [Defending Against Frequency-Based Attacks with Diffusion Models](https://mlsanity.com/paper/2504.11034/) (2025)
- [WildIng: A Wildlife Image Invariant Representation Model for Geographical Domain Shift](https://mlsanity.com/paper/2601.00993/) (2026)
- [Generalizable Multimodal Large Language Model Editing via Invariant Trajectory Learning](https://mlsanity.com/paper/2601.19700/) (2026)
- [BRIC: Bridging Kinematic Plans and Physical Control at Test Time](https://mlsanity.com/paper/2511.20431/) (2025)
- [Test-Time Modification: Inverse Domain Transformation for Robust Perception](https://mlsanity.com/paper/2512.13454/) (2025)
- [Mitigating Long-Tail Bias via Prompt-Controlled Diffusion Augmentation](https://mlsanity.com/paper/2602.04749/) (2026)
- [Miles: Metric Learning with Expandable Subspace for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2607.17593/) (2026)

## Abstract (arXiv)

Machine learning society has witnessed the emergence of a myriad of Out-of-Distribution (OoD) algorithms, which address the distribution shift between the training and the testing distribution by searching for a unified predictor or invariant feature representation. However, the task of directly mitigating the distribution shift in the unseen testing set is rarely investigated, due to the unavailability of the testing distribution during the training phase and thus the impossibility of training a distribution translator mapping between the training and testing distribution. In this paper, we explore how to bypass the requirement of testing distribution for distribution translator training and make the distribution translation useful for OoD prediction. We propose a portable Distribution Shift Inversion algorithm, in which, before being fed into the prediction model, the OoD testing samples are first linearly combined with additional Gaussian noise and then transferred back towards the training distribution using a diffusion model trained only on the source distribution. Theoretical analysis reveals the feasibility of our method. Experimental results, on both multiple-domain generalization datasets and single-domain generalization datasets, show that our method provides a general performance gain when plugged into a wide range of commonly used OoD algorithms.