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A Non-Adversarial Approach to Idempotent Generative Modelling

arXiv 2511.02614 ↗First posted 4 Nov 2025cs.LGcited by 0

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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.

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21 of 31 references.

References · 21

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,694
  3. 2018A Style-Based Generator Architecture for Generative Adversarial Networkscited by 5,986
  4. 2022Generative Adversarial Networkscited by 5,603
  5. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 925
  6. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  7. 2022Diffusion Models for Adversarial Purificationcited by 469
  8. 2020Reliable Fidelity and Diversity Metrics for Generative Modelscited by 425
  9. 2023Denoising Diffusion Models for Plug-and-Play Image Restorationcited by 335
  10. 2023Text-to-image Diffusion Models in Generative AI: A Surveycited by 264
  11. 2022Pretrained Language Models for Text Generation: A Surveycited by 121
  12. 2023Deep Learning on Implicit Neural Representations of Shapescited by 62
9 more
  1. 2024Advances in 3D Generation: A Surveycited by 62
  2. 2018Implicit Maximum Likelihood Estimationcited by 52
  3. 2019Overparameterized Neural Networks Implement Associative Memorycited by 45
  4. 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
  5. 2023Idempotent Generative Networkcited by 17
  6. 2024Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifoldscited by 13
  7. 2024Rejection Sampling IMLE: Designing Priors for Better Few-Shot Image Synthesiscited by 8
  8. 2022Semi-supervised domain adaptation with CycleGAN guided by a downstream task losscited by 4
  9. 2023How Good Are Deep Generative Models for Solving Inverse Problems?cited by 1

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