# A Non-Adversarial Approach to Idempotent Generative Modelling

arXiv: https://arxiv.org/abs/2511.02614 · HTML: https://mlsanity.com/paper/2511.02614/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 4 Nov 2025.

## Builds on (most cited first, 21 of 21)

- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Diffusion Models for Adversarial Purification](https://mlsanity.com/paper/2205.07460/) (2022)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Denoising Diffusion Models for Plug-and-Play Image Restoration](https://mlsanity.com/paper/2305.08995/) (2023)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [Pretrained Language Models for Text Generation: A Survey](https://mlsanity.com/paper/2201.05273/) (2022)
- [Deep Learning on Implicit Neural Representations of Shapes](https://mlsanity.com/paper/2302.05438/) (2023)
- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [Overparameterized Neural Networks Implement Associative Memory](https://mlsanity.com/paper/1909.12362/) (2019)
- [Can Push-forward Generative Models Fit Multimodal Distributions?](https://mlsanity.com/paper/2206.14476/) (2022)
- [Idempotent Generative Network](https://mlsanity.com/paper/2311.01462/) (2023)
- [Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds](https://mlsanity.com/paper/2410.12779/) (2024)
- [Rejection Sampling IMLE: Designing Priors for Better Few-Shot Image Synthesis](https://mlsanity.com/paper/2409.17439/) (2024)
- [Semi-supervised domain adaptation with CycleGAN guided by a downstream task loss](https://mlsanity.com/paper/2208.08815/) (2022)
- [How Good Are Deep Generative Models for Solving Inverse Problems?](https://mlsanity.com/paper/2312.12691/) (2023)

## Abstract (arXiv)

Idempotent Generative Networks (IGNs) are deep generative models that also function as local data manifold projectors, mapping arbitrary inputs back onto the manifold. They are trained to act as identity operators on the data and as idempotent operators off the data manifold. However, IGNs suffer from mode collapse, mode dropping, and training instability due to their objectives, which contain adversarial components and can cause the model to cover the data manifold only partially -- an issue shared with generative adversarial networks. We introduce Non-Adversarial Idempotent Generative Networks (NAIGNs) to address these issues. Our loss function combines reconstruction with the non-adversarial generative objective of Implicit Maximum Likelihood Estimation (IMLE). This improves on IGN's ability to restore corrupted data and generate new samples that closely match the data distribution. We moreover demonstrate that NAIGNs implicitly learn the distance field to the data manifold, as well as an energy-based model.