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1. Variational Pictures

   https://doi.org/10.1007/978-3-319-91376-6_9  

   Erwig, M.; Smeltzer, K. (May 2018, Int. Conf. on the Theory and Application of Diagrams)

   Diagrams and pictures are a powerful medium to communicate ideas, designs, and art. However, authors of pictures are forced to use rudimentary and ad hoc techniques in managing multiple variants of their creations, such as copying and renaming files or abusing layers in an advanced graphical editing tool. We propose a model of variational pictures as a basis for the design of editors and other tools for managing variation in pictures. This model enjoys a number of theoretical properties that support exploratory graphical design and can help systematize picture creators' workflows. 

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2. Provably Scalable Black-Box Variational Inference with Structured Variational Families

   Ko, Joohwan; Kim, Kyurae; Kim, Woo Chang; Gardner, Jacob R (July 2024, International Conference on Machine Learning (ICML 2024))
3. Denoising Diffusion Variational Inference: Diffusion Models as Expressive Variational Posteriors

   Piriyakulkij, Wasu; Wang, Yingheng; Kuleshov, Volodymyr (January 2025, AAAI)
4. Variational microcanonical estimator

   https://doi.org/10.1103/PhysRevResearch.5.033224  

   Pollock, Klée; Orth, Peter P.; Iadecola, Thomas (September 2023, Physical Review Research)
5. Variational Bayesian Quantization

   Yang, Yibo; Bamler, Robert; Mandt, Stephan (July 2020, Proceedings of Machine Learning Research)

   We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike current end-to-end neural compression methods that cater the model to a fixed quantization scheme, our algorithm separates model design and training from quantization. Consequently, our algorithm enables “plug-and-play” compression with variable rate-distortion trade-off, using a single trained model. Our algorithm can be seen as a novel extension of arithmetic coding to the continuous domain, and uses adaptive quantization accuracy based on estimates of posterior uncertainty. Our experimental results demonstrate the importance of taking into account posterior uncertainties, and show that image compression with the proposed algorithm outperforms JPEG over a wide range of bit rates using only a single standard VAE. Further experiments on Bayesian neural word embeddings demonstrate the versatility of the proposed method. 

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