# Detecting Deepfakes via Hamiltonian Dynamics

arXiv: https://arxiv.org/abs/2605.04405 · HTML: https://mlsanity.com/paper/2605.04405/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 61 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 30 of 47)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [FaceForensics++: Learning to Detect Manipulated Facial Images](https://mlsanity.com/paper/1901.08971/) (2019)
- [CNN-generated images are surprisingly easy to spot... for now](https://mlsanity.com/paper/1912.11035/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Face2Face: Real-time Face Capture and Reenactment of RGB Videos](https://mlsanity.com/paper/2007.14808/) (2020)
- [Celeb-DF: A Large-scale Challenging Dataset for DeepFake Forensics](https://mlsanity.com/paper/1909.12962/) (2019)
- [Thinking in Frequency: Face Forgery Detection by Mining Frequency-aware Clues](https://mlsanity.com/paper/2007.09355/) (2020)
- [Towards Universal Fake Image Detectors that Generalize Across Generative Models](https://mlsanity.com/paper/2302.10174/) (2023)
- [Face X-ray for More General Face Forgery Detection](https://mlsanity.com/paper/1912.13458/) (2019)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [DIRE for Diffusion-Generated Image Detection](https://mlsanity.com/paper/2303.09295/) (2023)
- [Detecting Deepfakes with Self-Blended Images](https://mlsanity.com/paper/2204.08376/) (2022)
- [PhySG: Inverse Rendering with Spherical Gaussians for Physics-based Material Editing and Relighting](https://mlsanity.com/paper/2104.00674/) (2021)
- [GenImage: A Million-Scale Benchmark for Detecting AI-Generated Image](https://mlsanity.com/paper/2306.08571/) (2023)
- [Generalizing Face Forgery Detection with High-frequency Features](https://mlsanity.com/paper/2103.12376/) (2021)
- [DeeperForensics-1.0: A Large-Scale Dataset for Real-World Face Forgery Detection](https://mlsanity.com/paper/2001.03024/) (2020)
- [Spatial-Phase Shallow Learning: Rethinking Face Forgery Detection in Frequency Domain](https://mlsanity.com/paper/2103.01856/) (2021)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [WildDeepfake: A Challenging Real-World Dataset for Deepfake Detection](https://mlsanity.com/paper/2101.01456/) (2021)
- [Inverse Rendering for Complex Indoor Scenes: Shape, Spatially-Varying Lighting and SVBRDF from a Single Image](https://mlsanity.com/paper/1905.02722/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Forgery-aware Adaptive Transformer for Generalizable Synthetic Image Detection](https://mlsanity.com/paper/2312.16649/) (2023)
- [UCF: Uncovering Common Features for Generalizable Deepfake Detection](https://mlsanity.com/paper/2304.13949/) (2023)
- [DeepfakeBench: A Comprehensive Benchmark of Deepfake Detection](https://mlsanity.com/paper/2307.01426/) (2023)
- [DF40: Toward Next-Generation Deepfake Detection](https://mlsanity.com/paper/2406.13495/) (2024)
- [Transcending Forgery Specificity with Latent Space Augmentation for Generalizable Deepfake Detection](https://mlsanity.com/paper/2311.11278/) (2023)

## Abstract (arXiv)

Driven by the rapid development of generative AI models, deepfake detectors are compelled to undergo periodic recalibration to capture newly developed synthetic artifacts. To break this cycle, we propose a new perspective on deepfake detection: moving from static pattern recognition to dynamical stability analysis. Specifically, our approach is motivated by physics-inspired priors: we hypothesize that natural images, as products of dissipative physical processes, tend to settle near stable, low-energy equilibria. In contrast, generative models optimize for statistical similarity to real images but do not explicitly enforce structural constraints such as geometric smoothness, leaving deepfakes more likely to occupy unstable, high-energy states. To operationalize this, we introduce Hamiltonian Action Anomaly Detection (HAAD), comprising three contributions: i) We model the image latent manifold as a potential energy surface. Under this hypothesis, real images are expected to produce basin-like low-energy responses, whereas fake images are more likely to induce high-potential, high-gradient responses. ii) We employ Hamiltonian-inspired dynamics as a stability probe. By releasing latent states from rest, samples near stable regions remain bounded, while high-gradient samples produce larger trajectory responses. iii) We quantify these dynamic behaviors through two trajectory statistics, ie, Hamiltonian action and energy dissipation. Extensive experiments show that HAAD outperforms evaluated state-of-the-art baselines on challenging cross-dataset transfer benchmarks, supporting a physics-inspired stability prior for digital forensics.