Wavelet Flow: Fast Training of High Resolution Normalizing Flows

Normalizing flows are a class of probabilistic generative models which allow for both fast density computation and efficient sampling and are effective at modelling complex distributions like images. A drawback among current methods is their significant training cost, sometimes requiring months of GPU training time to achieve state-of-the-art results. This paper introduces Wavelet Flow, a multi-scale, normalizing flow architecture based on wavelets. A Wavelet Flow has an explicit representation of signal scale that inherently includes models of lower resolution signals and conditional generation of higher resolution signals, i.e., super resolution. A major advantage of Wavelet Flow is the ability to construct generative models for high resolution data (e.g., 1024 x 1024 images) that are impractical with previous models. Furthermore, Wavelet Flow is competitive with previous normalizing flows in terms of bits per dimension on standard (low resolution) benchmarks while being up to 15x faster to train.

Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows

Normalizing flows transform a simple base distribution into a complex target distribution and have proved to be powerful models for data generation and density estimation. In this work, we propose a novel type of normalizing flow driven by a differential deformation of the continuous-time Wiener process. As a result, we obtain a rich time series model whose observable process inherits many of the appealing properties of its base process, such as efficient computation of likelihoods and marginals. Furthermore, our continuous treatment provides a natural framework for irregular time series with an independent arrival process, including straightforward interpolation. We illustrate the desirable properties of the proposed model on popular stochastic processes and demonstrate its superior flexibility to variational RNN and latent ODE baselines in a series of experiments on synthetic and real-world data.

Variational Hyper RNN for Sequence Modeling

In this work, we propose a novel probabilistic sequence model that excels at capturing high variability in time series data, both across sequences and within an individual sequence. Our method uses temporal latent variables to capture information about the underlying data pattern and dynamically decodes the latent information into modifications of weights of the base decoder and recurrent model. The efficacy of the proposed method is demonstrated on a range of synthetic and real-world sequential data that exhibit large scale variations, regime shifts, and complex dynamics.

Normalizing Flows: Introduction and Ideas

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.

Noise Flow: Noise Modeling with Conditional Normalizing Flows

Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a coarse approximation of real sensor noise. This paper introduces Noise Flow, a powerful and accurate noise model based on recent normalizing flow architectures. Noise Flow combines well-established basic parametric noise models (e.g., signal-dependent noise) with the flexibility and expressiveness of normalizing flow networks. The result is a single, comprehensive, compact noise model containing fewer than 2500 parameters yet able to represent multiple cameras and gain factors. Noise Flow dramatically outperforms existing noise models, with 0.42 nats/pixel improvement over the camera-calibrated noise level functions, which translates to 52% improvement in the likelihood of sampled noise. Noise Flow represents the first serious attempt to go beyond simple parametric models to one that leverages the power of deep learning and data-driven noise distributions.

Walking on Thin Air: Environment-Free Physics-based Markerless Motion Capture

We propose a generative approach to physics-based motion capture. Unlike prior attempts to incorporate physics into tracking that assume the subject and scene geometry are calibrated and known a priori, our approach is automatic and online. This distinction is important since calibration of the environment is often difficult, especially for motions with props, uneven surfaces, or outdoor scenes. The use of physics in this context provides a natural framework to reason about contact and the plausibility of recovered motions. We propose a fast data-driven parametric body model, based on linear-blend skinning, which decouples deformations due to pose, anthropometrics and body shape. Pose (and shape) parameters are estimated using robust ICP optimization with physics-based dynamic priors that incorporate contact. Contact is estimated from torque trajectories and predictions of which contact points were active. To our knowledge, this is the first approach to take physics into account without explicit {\em a priori} knowledge of the environment or body dimensions. We demonstrate effective tracking from a noisy single depth camera, improving on state-of-the-art results quantitatively and producing better qualitative results, reducing visual artifacts like foot-skate and jitter.

Two-Stream Convolutional Networks for Dynamic Texture Synthesis

We introduce a two-stream model for dynamic texture synthesis. Our model is based on pre-trained convolutional networks (ConvNets) that target two independent tasks: (i) object recognition, and (ii) optical flow prediction. Given an input dynamic texture, statistics of filter responses from the object recognition ConvNet encapsulate the per-frame appearance of the input texture, while statistics of filter responses from the optical flow ConvNet model its dynamics. To generate a novel texture, a randomly initialized input sequence is optimized to match the feature statistics from each stream of an example texture. Inspired by recent work on image style transfer and enabled by the two-stream model, we also apply the synthesis approach to combine the texture appearance from one texture with the dynamics of another to generate entirely novel dynamic textures. We show that our approach generates novel, high quality samples that match both the framewise appearance and temporal evolution of input texture. Finally, we quantitatively evaluate our texture synthesis approach with a thorough user study.

Find your Way by Observing the Sun and Other Semantic Cues

In this paper we present a robust, efficient and affordable approach to self-localization which does not require neither GPS nor knowledge about the appearance of the world. Towards this goal, we utilize freely available cartographic maps and derive a probabilistic model that exploits semantic cues in the form of sun direction, presence of an intersection, road type, speed limit as well as the ego-car trajectory in order to produce very reliable localization results. Our experimental evaluation shows that our approach can localize much faster (in terms of driving time) with less computation and more robustly than competing approaches, which ignore semantic information.

Building Proteins in a Day: Efficient 3D Molecular Reconstruction

Discovering the 3D atomic structure of molecules such as proteins and viruses is a fundamental research problem in biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D structures from 2D images. This paper addresses the challenging problem of 3D reconstruction from 2D Cryo-EM images. A new framework for estimation is introduced which relies on modern stochastic optimization techniques to scale to large datasets. We also introduce a novel technique which reduces the cost of evaluating the objective function during optimization by over five orders or magnitude. The net result is an approach capable of estimating 3D molecular structure from large scale datasets in about a day on a single workstation.

Microscopic Advances with Large-Scale Learning: Stochastic Optimization for Cryo-EM

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to reconstruct 3D structures from 2D images. This paper introduces the challenging Cryo-EM density estimation problem as a novel application for stochastic optimization techniques. Structure discovery is formulated as MAP estimation in a probabilistic latent-variable model, resulting in an optimization problem to which an array of seven stochastic optimization methods are applied. The methods are tested on both real and synthetic data, with some methods recovering reasonable structures in less than one epoch from a random initialization. Complex quasi-Newton methods are found to converge more slowly than simple gradient-based methods, but all stochastic methods are found to converge to similar optima. This method represents a major improvement over existing methods as it is significantly faster and is able to converge from a random initialization.