# Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences

arXiv: https://arxiv.org/abs/2603.20025 · HTML: https://mlsanity.com/paper/2603.20025/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 53 references that are in the map.
- First posted on arXiv 20 Mar 2026.

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

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Free-Form Image Inpainting with Gated Convolution](https://mlsanity.com/paper/1806.03589/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [DECAF: Generating Fair Synthetic Data Using Causally-Aware Generative Networks](https://mlsanity.com/paper/2110.12884/) (2021)
- [Free-form Video Inpainting with 3D Gated Convolution and Temporal PatchGAN](https://mlsanity.com/paper/1904.10247/) (2019)
- [Normalized Wasserstein Distance for Mixture Distributions with Applications in Adversarial Learning and Domain Adaptation](https://mlsanity.com/paper/1902.00415/) (2019)
- [Structure-preserving GANs](https://mlsanity.com/paper/2202.01129/) (2022)
- [Wasserstein Gradient Flows for Moreau Envelopes of f-Divergences in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2402.04613/) (2024)
- [Causal Adversarial Network for Learning Conditional and Interventional Distributions](https://mlsanity.com/paper/2008.11376/) (2020)
- [Conditional Generative Models are Provably Robust: Pointwise Guarantees for Bayesian Inverse Problems](https://mlsanity.com/paper/2303.15845/) (2023)
- [DenseGNN: universal and scalable deeper graph neural networks for high-performance property prediction in crystals and molecules](https://mlsanity.com/paper/2501.03278/) (2025)
- [Understanding GANs: the LQG Setting](https://mlsanity.com/paper/1710.10793/) (2017)
- [GINNs: Graph-Informed Neural Networks for Multiscale Physics](https://mlsanity.com/paper/2006.14807/) (2020)
- [Square Hellinger Subadditivity for Bayesian Networks and its Applications to Identity Testing](https://mlsanity.com/paper/1612.03164/) (2016)
- [Formulation and properties of a divergence used to compare probability measures without absolute continuity](https://mlsanity.com/paper/1911.07422/) (2019)
- [Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data](https://mlsanity.com/paper/2210.17230/) (2022)
- [Principled Knowledge Extrapolation with GANs](https://mlsanity.com/paper/2205.13444/) (2022)
- [Paired Wasserstein Autoencoders for Conditional Sampling](https://mlsanity.com/paper/2412.07586/) (2024)
- [GAT-GMM: Generative Adversarial Training for Gaussian Mixture Models](https://mlsanity.com/paper/2006.10293/) (2020)
- [Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributions](https://mlsanity.com/paper/2405.13962/) (2024)
- [Proximal optimal transport divergences](https://mlsanity.com/paper/2505.12097/) (2025)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)
- [Learning conditional distributions on continuous spaces](https://mlsanity.com/paper/2406.09375/) (2024)

## Abstract (arXiv)

We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including (f,Gamma)-divergences, we prove a new infimal subadditivity principle showing that, under suitable conditions, a global variational discrepancy is controlled by an average of family-level discrepancies aligned with the graph. In an additive regime, the surrogate is exact. This closes a theoretical gap in the literature; existing subadditivity results justify graph-informed adversarial learning for classical discrepancies, but not for interpolative divergences, where the usual factorization argument breaks down. In turn, we provide a justification for replacing a standard, graph-agnostic GAN with a monolithic discriminator by a graph-informed GAN (GiGAN) with localized family-level discriminators, without requiring the optimizer itself to factorize according to the graph. We also obtain parallel results for integral probability metrics and proximal optimal transport divergences, identify natural discriminator classes for which the theory applies, and present experiments showing improved stability and structural recovery relative to graph-agnostic baselines.