# Delta-AI: Local objectives for amortized inference in sparse graphical models

arXiv: https://arxiv.org/abs/2310.02423 · HTML: https://mlsanity.com/paper/2310.02423/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Builds on (most cited first, 24 of 24)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Improved Contrastive Divergence Training of Energy Based Models](https://mlsanity.com/paper/2012.01316/) (2020)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [GFlowNets and variational inference](https://mlsanity.com/paper/2210.00580/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [Tighter Variational Bounds are Not Necessarily Better](https://mlsanity.com/paper/1802.04537/) (2018)
- [Reweighted Wake-Sleep](https://mlsanity.com/paper/1406.2751/) (2014)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [A Variational Perspective on Generative Flow Networks](https://mlsanity.com/paper/2210.07992/) (2022)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [Learning to learn generative programs with Memoised Wake-Sleep](https://mlsanity.com/paper/2007.03132/) (2020)
- [Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data](https://mlsanity.com/paper/2111.13180/) (2021)
- [Hybrid Memoised Wake-Sleep: Approximate Inference at the Discrete-Continuous Interface](https://mlsanity.com/paper/2107.06393/) (2021)

## Built on by (most cited first, 7 of 7)

- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [Learning to Scale Logits for Temperature-Conditional GFlowNets](https://mlsanity.com/paper/2310.02823/) (2023)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [On Divergence Measures for Training GFlowNets](https://mlsanity.com/paper/2410.09355/) (2024)
- [Energy-based generator matching: A neural sampler for general state space](https://mlsanity.com/paper/2505.19646/) (2025)
- [Bifurcated Generative Flow Networks](https://mlsanity.com/paper/2406.01901/) (2024)
- [Information-Geometric Forward Policy Training in GFlowNets](https://mlsanity.com/paper/2608.03967/) (2026)

## Abstract (arXiv)

We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call Delta-amortized inference (Delta-AI). Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. This yields a local constraint that can be turned into a local loss in the style of generative flow networks (GFlowNets) that enables off-policy training but avoids the need to instantiate all the random variables for each parameter update, thus speeding up training considerably. The Delta-AI objective matches the conditional distribution of a variable given its Markov blanket in a tractable learned sampler, which has the structure of a Bayesian network, with the same conditional distribution under the target PGM. As such, the trained sampler recovers marginals and conditional distributions of interest and enables inference of partial subsets of variables. We illustrate Delta-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.