# Conservative objective models are a special kind of contrastive divergence-based energy model

arXiv: https://arxiv.org/abs/2304.03866 · HTML: https://mlsanity.com/paper/2304.03866/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 24 references that are in the map.
- First posted on arXiv 7 Apr 2023.

## Builds on (most cited first, 14 of 14)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)
- [Offline Model-Based Optimization via Normalized Maximum Likelihood Estimation](https://mlsanity.com/paper/2102.07970/) (2021)
- [Making Sense of Reinforcement Learning and Probabilistic Inference](https://mlsanity.com/paper/2001.00805/) (2020)

## Built on by (most cited first, 3 of 3)

- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization](https://mlsanity.com/paper/2401.02019/) (2024)
- [Denoising Diffusion Probabilistic Models for Hardware-Impaired Communications](https://mlsanity.com/paper/2309.08568/) (2023)

## Abstract (arXiv)

In this work we theoretically show that conservative objective models (COMs) for offline model-based optimisation (MBO) are a special kind of contrastive divergence-based energy model, one where the energy function represents both the unconditional probability of the input and the conditional probability of the reward variable. While the initial formulation only samples modes from its learned distribution, we propose a simple fix that replaces its gradient ascent sampler with a Langevin MCMC sampler. This gives rise to a special probabilistic model where the probability of sampling an input is proportional to its predicted reward. Lastly, we show that better samples can be obtained if the model is decoupled so that the unconditional and conditional probabilities are modelled separately.