mlsanityData to 14 Oct 2026

The Thermodynamic Variational Objective

arXiv 1907.00031 ↗First posted 28 Jun 2019cs.LG stat.MLcited by 26

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Abstract (arXiv)

We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We use the TVO to learn both discrete and continuous deep generative models and empirically demonstrate state of the art model and inference network learning.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Jun 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 8; 2023: 6; 2024: 3; 2025: 2; 2026: 1.

26 papers.

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  1. 2022GFlowNets and variational inferencecited by 106
  2. 2022DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latentscited by 104
  3. 2022Score-Based Diffusion meets Annealed Importance Samplingcited by 51
  4. 2023Information-Theoretic Diffusioncited by 44
  5. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  6. 2021Nested Variational Inferencecited by 14
  7. 2021Surrogate Likelihoods for Variational Annealed Importance Samplingcited by 14
  8. 2024Neural Thermodynamic Integration: Free Energies from Energy-based Diffusion Modelscited by 14
  9. 2023Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyondcited by 13
  10. 2021q-Paths: Generalizing the Geometric Annealing Path using Power Meanscited by 12
  11. 2022Multiple Importance Sampling ELBO and Deep Ensembles of Variational Approximationscited by 12
  12. 2023Adaptive Annealed Importance Sampling with Constant Rate Progresscited by 7
14 more
  1. 2021Learning Proposals for Probabilistic Programs with Inference Combinatorscited by 6
  2. 2022Bounding Evidence and Estimating Log-Likelihood in VAEcited by 6
  3. 2022Unsupervised representation learning with recognition-parametrised probabilistic modelscited by 5
  4. 2022Variational Open-Domain Question Answeringcited by 5
  5. 2022Fast Offline Policy Optimization for Large Scale Recommendationcited by 4
  6. 2021Variational Inference with Holder Boundscited by 3
  7. 2023Reparameterized Variational Rejection Samplingcited by 2
  8. 2024Differentiable Annealed Importance Sampling Minimizes The Symmetrized Kullback-Leibler Divergence Between Initial and Target Distributioncited by 2
  9. 2026TUBE: Tangent Upper Bound on Evidence for Discrete Diffusion Language Modelscited by 2
  10. 2023Estimating optimal PAC-Bayes bounds with Hamiltonian Monte Carlocited by 1
  11. 2025Globally Convergent Variational Inferencecited by 1
  12. 2023Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencodercited by 0
  13. 2024Towards Model-Agnostic Posterior Approximation for Fast and Accurate Variational Autoencoderscited by 0
  14. 2025Tight Bounds for Jensen's Gap with Applications to Variational Inferencecited by 0