Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows

By R. Cornish, Anthony L. Caterini, George Deligiannidis, Arnaud Doucet. 2019

146 citations recorded by the source corpus.

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In Generative Models

Citations in the corpus

Stochastic Normalizing Flows (2020, background): “, if the sample space is restricted to a non-trivial Lie group [11, 12], another practical problem are induced Bi-Lipschitz constraints resulting from mapping uni-modal base distributions onto wellseparated multi-modal target distributions[4].”
Normalizing Flows for Probabilistic Modeling and Inference (2019, background): “Cornish et al. (2019) make due by performing variational inference, introducing an approximation q(z |x) that then allows for optimization via a lower bound on log px(x).”
Generalized Energy Based Models (2020, background): “In IGMs, such a GANs, the latent noise η is usually unimodal thus requiring a more sophisticated generator to distort a unimodal noise distribution into a distribution with multiple modes, as shown by Cornish et al. (2020).”
Diffusion Models: A Comprehensive Survey of Methods and Applications (2022, background): “Unfortunately, the bijective requirement also has limitations on modeling complex data, both empirically and theoretically [39, 243].”
The Power Spherical distribution (2020, background): “Davidson et al. (2019) addressed some of these issues and for future work, it could be promising to explore such direction further.”
A RAD approach to deep mixture models (2019, background): “This contrasts with Cornish et al. (2020), which uses instead continuous indexing for k but relies as a consequence on approximate variational inference for training their resulting model.”
Diffusion Normalizing Flow (2021, background): “However, the bijective requirement poses limitations on modeling complex data, both empirically and theoretically [42, 6].”
BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery (2021, methodology): “We use continuously indexed normalizing flows [10], a recently-developed family of flows offering good performance on multimodal densities.”
Implicit Normalizing Flows (2021, background): “In parallel with architecture design, Chen et al. (2020); Huang et al. (2020); Cornish et al. (2020); Nielsen et al. (2020) improve the capacity of NFs by operating in a higher-dimensional space.”