# Wasserstein Distance Rivals Kullback-Leibler Divergence for Knowledge Distillation

arXiv: https://arxiv.org/abs/2412.08139 · HTML: https://mlsanity.com/paper/2412.08139/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 58 of its 83 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 58)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [Relational Knowledge Distillation](https://mlsanity.com/paper/1904.05068/) (2019)
- [Contrastive Representation Distillation](https://mlsanity.com/paper/1910.10699/) (2019)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)

## Built on by (most cited first, 19 of 19)

- [ABKD: Pursuing a Proper Allocation of the Probability Mass in Knowledge Distillation via α-β-Divergence](https://mlsanity.com/paper/2505.04560/) (2025)
- [Machine Unlearning under Retain-Forget Entanglement](https://mlsanity.com/paper/2603.26569/) (2026)
- [Simple yet Effective Semi-supervised Knowledge Distillation from Vision-Language Models via Dual-Head Optimization](https://mlsanity.com/paper/2505.07675/) (2025)
- [Generative Distribution Distillation](https://mlsanity.com/paper/2507.14503/) (2025)
- [Privacy-Aware Continual Self-Supervised Learning on Multi-Window Chest Computed Tomography for Domain-Shift Robustness](https://mlsanity.com/paper/2510.27213/) (2025)
- [Structural and Statistical Audio Texture Knowledge Distillation for Acoustic Classification](https://mlsanity.com/paper/2501.01921/) (2025)
- [KD2M: A unifying framework for feature knowledge distillation](https://mlsanity.com/paper/2504.01757/) (2025)
- [TopKD: Top-scaled Knowledge Distillation](https://mlsanity.com/paper/2508.04539/) (2025)
- [Multi-Worker Selection based Distributed Swarm Learning for Edge IoT with Non-i.i.d. Data](https://mlsanity.com/paper/2509.18367/) (2025)
- [Approaching Low-Cost Cardiac Intelligence with Semi-Supervised Knowledge Distillation](https://mlsanity.com/paper/2511.02851/) (2025)
- [Cascaded Transfer: Learning Many Tasks under Budget Constraints](https://mlsanity.com/paper/2601.21513/) (2026)
- [BicKD: Bilateral Contrastive Knowledge Distillation](https://mlsanity.com/paper/2602.01265/) (2026)
- [The Bridge-Garden Dilemma in LLM Distillation: Why Mixing Hard and Soft Labels Works](https://mlsanity.com/paper/2605.26246/) (2026)
- [Cross-Modal Knowledge Distillation without Paired Data: Theoretical Foundation and Algorithm](https://mlsanity.com/paper/2606.10504/) (2026)
- [A Unified Approach to Interpreting Knowledge Distillation for Large Language Models via Interactions](https://mlsanity.com/paper/2607.08776/) (2026)
- [Do We Really Need Multimodal Emotion Language Models Larger Than 1B Parameters?](https://mlsanity.com/paper/2607.12787/) (2026)
- [ReDraft, Don't Just Distill: Reference-Driven Revision for Continual VLLM Post-Training](https://mlsanity.com/paper/2609.16639/) (2026)
- [Distilling What Matters: Confidence-Aware Selective Distillation for Large Language Models](https://mlsanity.com/paper/2609.36734/) (2026)
- [A 3GPP-Compliant Benchmark Dataset for RIS-Aided Beyond 5G Networks](https://mlsanity.com/paper/2609.39058/) (2026)

## Abstract (arXiv)

Since pioneering work of Hinton et al., knowledge distillation based on Kullback-Leibler Divergence (KL-Div) has been predominant, and recently its variants have achieved compelling performance. However, KL-Div only compares probabilities of the corresponding category between the teacher and student while lacking a mechanism for cross-category comparison. Besides, KL-Div is problematic when applied to intermediate layers, as it cannot handle non-overlapping distributions and is unaware of geometry of the underlying manifold. To address these downsides, we propose a methodology of Wasserstein Distance (WD) based knowledge distillation. Specifically, we propose a logit distillation method called WKD-L based on discrete WD, which performs cross-category comparison of probabilities and thus can explicitly leverage rich interrelations among categories. Moreover, we introduce a feature distillation method called WKD-F, which uses a parametric method for modeling feature distributions and adopts continuous WD for transferring knowledge from intermediate layers. Comprehensive evaluations on image classification and object detection have shown (1) for logit distillation WKD-L outperforms very strong KL-Div variants; (2) for feature distillation WKD-F is superior to the KL-Div counterparts and state-of-the-art competitors. The source code is available at https://peihuali.org/WKD