Despite substantial progress in signal source separation, results for richly structured data continue to contain perceptible artifacts. In contrast, recent deep generative models can produce authentic samples in a variety of domains that are indistinguishable from samples of the data distribution. This paper introduces a Bayesian approach to source separation that uses generative models as priors over the components of a mixture of sources, and noise-annealed Langevin dynamics to sample from the posterior distribution of sources given a mixture. This decouples the source separation problem from generative modeling, enabling us to directly use cutting-edge generative models as priors. The method achieves state-of-the-art performance for MNIST digit separation. We introduce new methodology for evaluating separation quality on richer datasets, providing quantitative evaluation of separation results on CIFAR-10. We also provide qualitative results on LSUN.
We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we argue that it might be advantageous to use more flexible code distributions. We demonstrate how these distributions can be induced directly from the data. The benefits include: more powerful generative models, better modeling of latent structure and explicit control of the degree of generalization.
Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and that of the data distribution, a problem found in widely used deep generative models such as VAEs and Glow. While a typical choice for a prior distribution is a standard Gaussian distribution, properties of distributions of real data sets may not be consistent with a unimodal prior distribution. This paper focuses on the relationship between the choice of a …
Prior-Fitted Functional Flow: In-Context Generative Models for Pharmacokinetics
University of Potsdam（波恩大学）；Technical University Berlin（柏林技术大学）；Freie Universität Berlin（柏林自由大学）；University of Bonn（波恩大学）；NHETC, Rutgers University（Rutgers大学国家健康教育与培训中心）
PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling
University of Oxford（牛津大学）；Aalto University（阿尔托大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；University of Copenhagen（哥本哈根大学）；Imperial College London（伦敦帝国学院）
We assume that a high-dimensional datum, like an image, is a compositional expression of a set of properties, with a complicated non-linear relationship between the datum and its properties. This paper proposes a factorial mixture prior for capturing latent properties, thereby adding structured compositionality to deep generative models. The prior treats a latent vector as belonging to Cartesian product of subspaces, each of which is quantized separately with a Gaussian mixture model. Some mixture components can be set to represent properties as observed random variables whenever labeled prope…
Harvard University（哈佛大学）；QuEra Computing Inc.（QuEra计算公司）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely-used generative models, known as Bayesian networks, and its minimal quantum extension. We …
Queen Mary University of London（伦敦玛丽女王大学）；The University of Sheffield（谢菲尔德大学）
Gaussian process (GP) audio source separation is a time-domain approach that circumvents the inherent phase approximation issue of spectrogram based methods. Furthermore, through its kernel, GPs elegantly incorporate prior knowledge about the sources into the separation model. Despite these compelling advantages, the computational complexity of GP inference scales cubically with the number of audio samples. As a result, source separation GP models have been restricted to the analysis of short audio frames. We introduce an efficient application of GPs to time-domain audio source separation, wit…
Federated Learning for Non-factorizable Models using Deep Generative Prior Approximations
Centre for Data Science, Queensland University of Technology（昆士兰科技大学数据科学中心）；School of Mathematical Sciences, Queensland University of Technology（昆士兰科技大学数学科学学院）；CEREMADE, Université Paris-Dauphine（巴黎第九大学CEREMADE研究中心）；Imperial College London（伦敦帝国学院）；Euler Institute, Università della Svizzera italiana (USI)（瑞士意大利语区大学欧拉研究所）；Insubria University（因苏布里亚大学）
We present an application of deep generative models in the context of partial-differential equation (PDE) constrained inverse problems. We combine a generative adversarial network (GAN) representing an a priori model that creates subsurface geological structures and their petrophysical properties, with the numerical solution of the PDE governing the propagation of acoustic waves within the earth's interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm (MALA) to sample from the posterior given seismic observations. Gradients with respect to the model…
Arizona State University（亚利桑那州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
In this paper, we develop a Wasserstein autoencoder (WAE) with a hyperspherical prior for multimodal data in the application of inertial confinement fusion. Unlike a typical hyperspherical generative model that requires computationally inefficient sampling from distributions like the von Mis Fisher, we sample from a normal distribution followed by a projection layer before the generator. Finally, to determine the validity of the generated samples, we exploit a known relationship between the modalities in the dataset as a scientific constraint, and study different properties of the proposed mod…
Northwestern University（西北大学）；Argonne National Laboratory（阿贡国家实验室）
Ptychography is a well-established coherent diffraction imaging technique that enables non-invasive imaging of samples at a nanometer scale. It has been extensively used in various areas such as the defense industry or materials science. One major limitation of ptychography is the long data acquisition time due to mechanical scanning of the sample; therefore, approaches to reduce the scan points are highly desired. However, reconstructions with less number of scan points lead to imaging artifacts and significant distortions, hindering a quantitative evaluation of the results. To address this b…
In logistic regression, separation occurs when a linear combination of the predictors can perfectly classify part or all of the observations in the sample, and as a result, finite maximum likelihood estimates of the regression coefficients do not exist. Gelman et al. (2008) recommended independent Cauchy distributions as default priors for the regression coefficients in logistic regression, even in the case of separation, and reported posterior modes in their analyses. As the mean does not exist for the Cauchy prior, a natural question is whether the posterior means of the regression coefficie…
Generative source separation methods such as non-negative matrix factorization (NMF) or auto-encoders, rely on the assumption of an output probability density. Generative Adversarial Networks (GANs) can learn data distributions without needing a parametric assumption on the output density. We show on a speech source separation experiment that, a multi-layer perceptron trained with a Wasserstein-GAN formulation outperforms NMF, auto-encoders trained with maximum likelihood, and variational auto-encoders in terms of source to distortion ratio.
This paper introduces and solves the simultaneous source separation and phase retrieval (S$^3$PR) problem. S$^3$PR is an important but largely unsolved problem in a number application domains, including microscopy, wireless communication, and imaging through scattering media, where one has multiple independent coherent sources whose phase is difficult to measure. In general, S$^3$PR is highly under-determined, non-convex, and difficult to solve. In this work, we demonstrate that by restricting the solutions to lie in the range of a deep generative model, we can constrain the search space suffi…
Insilico Medicine（英矽智能）；National Research University Higher School of Economics（俄罗斯国立高等经济研究大学）
Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard Gaussian distribution as a prior. Previous works show that the richer family of prior distributions may help to avoid the mode collapse problem in GANs and to improve the evidence lower bound in VAEs. We propose a new family of prior distributions---Tensor Ring Induced Prior (TRIP)---that packs an exponential number of Gaussians into a high-dimensional lattice …
NTT Communication Science Laboratories, NTT Corporation（NTT 公司 NTT 通信科学实验室）；University of Tsukuba（筑波大学）
This paper proposes a multichannel source separation technique called the multichannel variational autoencoder (MVAE) method, which uses a conditional VAE (CVAE) to model and estimate the power spectrograms of the sources in a mixture. By training the CVAE using the spectrograms of training examples with source-class labels, we can use the trained decoder distribution as a universal generative model capable of generating spectrograms conditioned on a specified class label. By treating the latent space variables and the class label as the unknown parameters of this generative model, we can deve…
Amsterdam Machine Learning Lab（阿姆斯特丹机器学习实验室）；University of Amsterdam（阿姆斯特丹大学）
Recent advancements in deep generative modeling make it possible to learn prior distributions from complex data that subsequently can be used for Bayesian inference. However, we find that distributions learned by deep generative models for audio signals do not exhibit the right properties that are necessary for tasks like audio source separation using a probabilistic approach. We observe that the learned prior distributions are either discriminative and extremely peaked or smooth and non-discriminative. We quantify this behavior for two types of deep generative models on two audio datasets.
Iowa State University（爱荷华州立大学）；New York University（纽约大学）
Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. In this paper, we introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generativ…
University of Surrey（萨里大学）；Tencent AI lab（腾讯人工智能实验室）
Single-channel signal separation and deconvolution aims to separate and deconvolve individual sources from a single-channel mixture and is a challenging problem in which no prior knowledge of the mixing filters is available. Both individual sources and mixing filters need to be estimated. In addition, a mixture may contain non-stationary noise which is unseen in the training set. We propose a synthesizing-decomposition (S-D) approach to solve the single-channel separation and deconvolution problem. In synthesizing, a generative model for sources is built using a generative adversarial network …
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm for random Gaussian measurements (practically relevant in imaging through scattering media) and Fourier friendly measurements (relevant in optical set ups). We demonstrate that proposed approach achieves impressive results when compared with traditional hand engineered priors including sparsity and denoising frameworks for number of measurements and robustn…
Multiple stains are usually used to highlight biological substances in biomedical image analysis. To decompose multiple stains for co-localization quantification, blind source separation is usually performed. Prior model-based stain separation methods usually rely on stains' spatial distributions over an image and may fail to solve the co-localization problem. With the advantage of machine learning, deep generative models are used for this purpose. Since prior knowledge of imaging models is ignored in purely data-driven solutions, these methods may be sub-optimal. In this study, a novel learni…
University of Science and Technology of China（中国科学技术大学）；Beijing Jiaotong University（北京交通大学）；Institute of Automation, CAS（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Generative Adversarial Network(GAN) provides a good generative framework to produce realistic samples, but suffers from two recognized issues as mode collapse and unstable training. In this work, we propose to employ explicit manifold learning as prior to alleviate mode collapse and stabilize training of GAN. Since the basic assumption of conventional manifold learning fails in case of sparse and uneven data distribution, we introduce a new target, Minimum Manifold Coding (MMC), for manifold learning to encourage simple and unfolded manifold. In essence, MMC is the general case of the shortest…
The Generator of a Generative Adversarial Network (GAN) is trained to transform latent vectors drawn from a prior distribution into realistic looking photos. These latent vectors have been shown to encode information about the content of their corresponding images. Projecting input images onto the latent space of a GAN is non-trivial, but previous work has successfully performed this task for latent spaces with a uniform prior. We extend these techniques to latent spaces with a Gaussian prior, and demonstrate our technique's effectiveness.
In this paper, we are interested in audio-visual speech separation given a single-channel audio recording as well as visual information (lips movements) associated with each speaker. We propose an unsupervised technique based on audio-visual generative modeling of clean speech. More specifically, during training, a latent variable generative model is learned from clean speech spectrograms using a variational auto-encoder (VAE). To better utilize the visual information, the posteriors of the latent variables are inferred from mixed speech (instead of clean speech) as well as the visual data. Th…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Institute of Mathematics for Industry, Kyushu University（九州大学产业数学研究所）
Prior domain knowledge can greatly help to learn generative models. However, it is often too costly to hard-code prior knowledge as a specific model architecture, so we often have to use general-purpose models. In this paper, we propose a method to incorporate prior knowledge of feature relations into the learning of general-purpose generative models. To this end, we formulate a regularizer that makes the marginals of a generative model to follow prescribed relative dependence of features. It can be incorporated into off-the-shelf learning methods of many generative models, including variation…
The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work, we study the algorithmic aspects of such a learning-based approach from a theoretical perspective. For certain generative network architectures, we establish a simple non-convex algorithmic approach that (a) theoretically enjoys linear convergence guarantees for certain inverse problems, and (b) empirically improves upon conventional techniques such as back…
A method for unsupervised contextual anomaly detection is proposed using a cross-linked pair of Variational Auto-Encoders for assigning a normality score to an observation. The method enables a distinct separation of contextual from behavioral attributes and is robust to the presence of anomalous or novel contextual attributes. The method can be trained with data sets that contain anomalies without any special pre-processing.
Separating two sources from an audio mixture is an important task with many applications. It is a challenging problem since only one signal channel is available for analysis. In this paper, we propose a novel framework for singing voice separation using the generative adversarial network (GAN) with a time-frequency masking function. The mixture spectra is considered to be a distribution and is mapped to the clean spectra which is also considered a distribtution. The approximation of distributions between mixture spectra and clean spectra is performed during the adversarial training process. In…
BI Norwegian Business School（BI挪威商学院）；UiT The Arctic University of Norway（挪威北极大学）；Norwegian Computing Center（挪威计算中心）
Deep generative models with latent variables have been used lately to learn joint representations and generative processes from multi-modal data. These two learning mechanisms can, however, conflict with each other and representations can fail to embed information on the data modalities. This research studies the realistic scenario in which all modalities and class labels are available for model training, but where some modalities and labels required for downstream tasks are missing. We show, in this scenario, that the variational lower bound limits mutual information between joint representat…
LINE Corporation（LINE公司）；Naver Corporation（NAVER公司）
We propose DiffSep, a new single channel source separation method based on score-matching of a stochastic differential equation (SDE). We craft a tailored continuous time diffusion-mixing process starting from the separated sources and converging to a Gaussian distribution centered on their mixture. This formulation lets us apply the machinery of score-based generative modelling. First, we train a neural network to approximate the score function of the marginal probabilities or the diffusion-mixing process. Then, we use it to solve the reverse time SDE that progressively separates the sources …
Despite phenomenal progress in recent years, state-of-the-art music separation systems produce source estimates with significant perceptual shortcomings, such as adding extraneous noise or removing harmonics. We propose a post-processing model (the Make it Sound Good (MSG) post-processor) to enhance the output of music source separation systems. We apply our post-processing model to state-of-the-art waveform-based and spectrogram-based music source separators, including a separator unseen by MSG during training. Our analysis of the errors produced by source separators shows that waveform model…
We showcase an unsupervised method that repurposes deep models trained for music generation and music tagging for audio source separation, without any retraining. An audio generation model is conditioned on an input mixture, producing a latent encoding of the audio used to generate audio. This generated audio is fed to a pretrained music tagger that creates source labels. The cross-entropy loss between the tag distribution for the generated audio and a predefined distribution for an isolated source is used to guide gradient ascent in the (unchanging) latent space of the generative model. This …
We focus on generative autoencoders, such as variational or adversarial autoencoders, which jointly learn a generative model alongside an inference model. Generative autoencoders are those which are trained to softly enforce a prior on the latent distribution learned by the inference model. We call the distribution to which the inference model maps observed samples, the learned latent distribution, which may not be consistent with the prior. We formulate a Markov chain Monte Carlo (MCMC) sampling process, equivalent to iteratively decoding and encoding, which allows us to sample from the learn…
This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustness against noise, using far fewer samples. We further modify the proposed approach to allow the generative model to explore solutions outside the range, leading to improved performance.
We study compressive sensing with a deep generative network prior. Initial theoretical guarantees for efficient recovery from compressed linear measurements have been developed for signals in the range of a ReLU network with Gaussian weights and logarithmic expansivity: that is when each layer is larger than the previous one by a logarithmic factor. It was later shown that constant expansivity is sufficient for recovery. It has remained open whether the expansivity can be relaxed, allowing for networks with contractive layers (as often the case of real generators). In this work we answer this …
University of Minnesota, Twin Cities（明尼苏达大学双城分校）；University of Oxford（牛津大学）
Several deep learning methods for phase retrieval exist, but most of them fail on realistic data without precise support information. We propose a novel method based on single-instance deep generative prior that works well on complex-valued crystal data.
Department of Computer Science and Engineering, Washington University in St. Louis（圣路易斯华盛顿大学计算机科学与工程系）；Department of Electrical and Systems Engineering, Washington University in St. Louis（圣路易斯华盛顿大学电气与系统工程系）；Department of Bioengineering, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校生物工程系）
Medical image reconstruction is typically an ill-posed inverse problem. In order to address such ill-posed problems, the prior distribution of the sought after object property is usually incorporated by means of some sparsity-promoting regularization. Recently, prior distributions for images estimated using generative adversarial networks (GANs) have shown great promise in regularizing some of these image reconstruction problems. In this work, we apply an image-adaptive GAN-based reconstruction method (IAGAN) to reconstruct high fidelity images from incomplete medical imaging data. It is obser…
National University of Singapore（新加坡国立大学）；Indian Institute of Technology (IIT) Kanpur（印度理工学院坎普尔分校）
The goal of standard 1-bit compressive sensing is to accurately recover an unknown sparse vector from binary-valued measurements, each indicating the sign of a linear function of the vector. Motivated by recent advances in compressive sensing with generative models, where a generative modeling assumption replaces the usual sparsity assumption, we study the problem of 1-bit compressive sensing with generative models. We first consider noiseless 1-bit measurements, and provide sample complexity bounds for approximate recovery under i.i.d.~Gaussian measurements and a Lipschitz continuous generati…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Washington（华盛顿大学）；Pohang University of Science and Technology（浦项科技大学）
Federated Learning (FL) is a distributed learning framework, in which the local data never leaves clients devices to preserve privacy, and the server trains models on the data via accessing only the gradients of those local data. Without further privacy mechanisms such as differential privacy, this leaves the system vulnerable against an attacker who inverts those gradients to reveal clients sensitive data. However, a gradient is often insufficient to reconstruct the user data without any prior knowledge. By exploiting a generative model pretrained on the data distribution, we demonstrate that…
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the specification that a variable should lie in the range of a neural network. This is motivated by recent successful applications of Generative Adversarial Networks (GANs) in tasks like compressive sensing, denoising and robustness against adversarial examples. The derived rates for our algorithm are characterized in terms of certain geometric properties of the gen…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；Misubishi Electric Research Laboratories（三菱电机研究实验室）；Arizona State University（亚利桑那州立大学）
In this paper, we propose the generative patch prior (GPP) that defines a generative prior for compressive image recovery, based on patch-manifold models. Unlike learned, image-level priors that are restricted to the range space of a pre-trained generator, GPP can recover a wide variety of natural images using a pre-trained patch generator. Additionally, GPP retains the benefits of generative priors like high reconstruction quality at extremely low sensing rates, while also being much more generally applicable. We show that GPP outperforms several unsupervised and supervised techniques on thre…
Institut de Physique Théorique CNRS & CEA & Université Paris-Saclay（法国国家科学研究中心、法国原子能与替代能源委员会及巴黎-萨克雷大学理论物理研究所）
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm for an ensemble of generative priors consisting of fully connected deep neural networks with random weight matrices and arbitrary activations. We compare the performance to sparse separable priors and conclude that generative priors might be advantageous in terms of algorithmic performance. In particular, while sparsity does not allow to perform compressive…
Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Amazon（亚马逊）；AWS AI Labs（AWS人工智能实验室）
In this work, we initiate the idea of using denoising diffusion models to learn priors for online decision making problems. Our special focus is on the meta-learning for bandit framework, with the goal of learning a strategy that performs well across bandit tasks of a same class. To this end, we train a diffusion model that learns the underlying task distribution and combine Thompson sampling with the learned prior to deal with new tasks at test time. Our posterior sampling algorithm is designed to carefully balance between the learned prior and the noisy observations that come from the learne…
The CSGM framework (Bora-Jalal-Price-Dimakis'17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for example, human faces and MNIST digits), and it is known to perform poorly on out-of-distribution samples. In this paper, we present the first successful application of the CSGM framework on clinical MRI data. We train a generative prior on brain scans from the fastMRI dataset, and show that posterior sampling via Langevin dynamics achieves high quality reconstructi…
