# Implicit Maximum Likelihood Estimation

arXiv: https://arxiv.org/abs/1809.09087 · HTML: https://mlsanity.com/paper/1809.09087/

## Key facts

- Cited by 52 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2018.

## Built on by (most cited first, 30 of 52)

- [Diffusion-SDF: Text-to-Shape via Voxelized Diffusion](https://mlsanity.com/paper/2212.03293/) (2022)
- [Balancing Act: Distribution-Guided Debiasing in Diffusion Models](https://mlsanity.com/paper/2402.18206/) (2024)
- [Truncated Diffusion Probabilistic Models and Diffusion-based Adversarial Auto-Encoders](https://mlsanity.com/paper/2202.09671/) (2022)
- [Social-Implicit: Rethinking Trajectory Prediction Evaluation and The Effectiveness of Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2203.03057/) (2022)
- [SCADE: NeRFs from Space Carving with Ambiguity-Aware Depth Estimates](https://mlsanity.com/paper/2303.13582/) (2023)
- [DiffFacto: Controllable Part-Based 3D Point Cloud Generation with Cross Diffusion](https://mlsanity.com/paper/2305.01921/) (2023)
- [MoFlow: One-Step Flow Matching for Human Trajectory Forecasting via Implicit Maximum Likelihood Estimation based Distillation](https://mlsanity.com/paper/2503.09950/) (2025)
- [Dual Contrastive Loss and Attention for GANs](https://mlsanity.com/paper/2103.16748/) (2021)
- [Green Learning: Introduction, Examples and Outlook](https://mlsanity.com/paper/2210.00965/) (2022)
- [From Latent Graph to Latent Topology Inference: Differentiable Cell Complex Module](https://mlsanity.com/paper/2305.16174/) (2023)
- [A Survey on Generative Modeling with Limited Data, Few Shots, and Zero Shot](https://mlsanity.com/paper/2307.14397/) (2023)
- [CabiNet: Scaling Neural Collision Detection for Object Rearrangement with Procedural Scene Generation](https://mlsanity.com/paper/2304.09302/) (2023)
- [Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction](https://mlsanity.com/paper/2111.06636/) (2021)
- [T2TD: Text-3D Generation Model based on Prior Knowledge Guidance](https://mlsanity.com/paper/2305.15753/) (2023)
- [Text-to-3D Shape Generation](https://mlsanity.com/paper/2403.13289/) (2024)
- [IMLE Policy: Fast and Sample Efficient Visuomotor Policy Learning via Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/2502.12371/) (2025)
- [PixelTransformer: Sample Conditioned Signal Generation](https://mlsanity.com/paper/2103.15813/) (2021)
- [Rejection Sampling IMLE: Designing Priors for Better Few-Shot Image Synthesis](https://mlsanity.com/paper/2409.17439/) (2024)
- [StEP: Style-based Encoder Pre-training for Multi-modal Image Synthesis](https://mlsanity.com/paper/2104.07098/) (2021)
- [VDSM: Unsupervised Video Disentanglement with State-Space Modeling and Deep Mixtures of Experts](https://mlsanity.com/paper/2103.07292/) (2021)
- [TPA3D: Triplane Attention for Fast Text-to-3D Generation](https://mlsanity.com/paper/2312.02647/) (2023)
- [Increasing the Utility of Synthetic Images through Chamfer Guidance](https://mlsanity.com/paper/2508.10631/) (2025)
- [PAGER: Progressive Attribute-Guided Extendable Robust Image Generation](https://mlsanity.com/paper/2206.00162/) (2022)
- [GENHOP: An Image Generation Method Based on Successive Subspace Learning](https://mlsanity.com/paper/2210.03689/) (2022)
- [CHIMLE: Conditional Hierarchical IMLE for Multimodal Conditional Image Synthesis](https://mlsanity.com/paper/2211.14286/) (2022)
- [Explorative Modeling: Unlocking a Third Pretraining Axis and End-to-End Generation](https://mlsanity.com/paper/2607.27372/) (2026)
- [Contrastive Mixture of Posteriors for Counterfactual Inference, Data Integration and Fairness](https://mlsanity.com/paper/2106.08161/) (2021)
- [Cluster-guided Image Synthesis with Unconditional Models](https://mlsanity.com/paper/2112.12911/) (2021)
- [ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Field](https://mlsanity.com/paper/2401.08140/) (2024)
- [WIMLE: Uncertainty-Aware World Models with IMLE for Sample-Efficient Continuous Control](https://mlsanity.com/paper/2602.14351/) (2026)

## Abstract (arXiv)

Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models that does not require knowledge of the form of the likelihood function or any derived quantities, but can be shown to be equivalent to maximizing likelihood under some conditions. Our result holds in the non-asymptotic parametric setting, where both the capacity of the model and the number of data examples are finite. We also demonstrate encouraging experimental results.