Didrik Nielsen

Giorgio Giannone, Didrik Nielsen, Ole Winther · mit

Denoising diffusion probabilistic models (DDPM) are powerful hierarchical latent variable models with remarkable sample generation quality and training stability. These properties can be attributed to parameter sharing in the generative hierarchy, as well as a parameter-free diffusion-based inference procedure. In this paper, we present Few-Shot Diffusion Models (FSDM), a framework for few-shot generation leveraging conditional DDPMs. FSDMs are trained to adapt the generative process conditioned on a small set of images from a given class by aggregating image patch information using a set-based Vision Transformer (ViT). At test time, the model is able to generate samples from previously unseen classes conditioned on as few as 5 samples from that class. We empirically show that FSDM can perform few-shot generation and transfer to new datasets. We benchmark variants of our method on complex vision datasets for few-shot learning and compare to unconditional and conditional DDPM baselines. Additionally, we show how conditioning the model on patch-based input set information improves training convergence.

Tobias Höppe, Arash Mehrjou, Stefan Bauer et al.

Predicting and anticipating future outcomes or reasoning about missing information in a sequence are critical skills for agents to be able to make intelligent decisions. This requires strong, temporally coherent generative capabilities. Diffusion models have shown remarkable success in several generative tasks, but have not been extensively explored in the video domain. We present Random-Mask Video Diffusion (RaMViD), which extends image diffusion models to videos using 3D convolutions, and introduces a new conditioning technique during training. By varying the mask we condition on, the model is able to perform video prediction, infilling, and upsampling. Due to our simple conditioning scheme, we can utilize the same architecture as used for unconditional training, which allows us to train the model in a conditional and unconditional fashion at the same time. We evaluate RaMViD on two benchmark datasets for video prediction, on which we achieve state-of-the-art results, and one for video generation. High-resolution videos are provided at https://sites.google.com/view/video-diffusion-prediction.

Emiel Hoogeboom, Didrik Nielsen, Priyank Jaini et al.

Generative flows and diffusion models have been predominantly trained on ordinal data, for example natural images. This paper introduces two extensions of flows and diffusion for categorical data such as language or image segmentation: Argmax Flows and Multinomial Diffusion. Argmax Flows are defined by a composition of a continuous distribution (such as a normalizing flow), and an argmax function. To optimize this model, we learn a probabilistic inverse for the argmax that lifts the categorical data to a continuous space. Multinomial Diffusion gradually adds categorical noise in a diffusion process, for which the generative denoising process is learned. We demonstrate that our method outperforms existing dequantization approaches on text modelling and modelling on image segmentation maps in log-likelihood.

Priyank Jaini, Didrik Nielsen, Max Welling

Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. However, a major limitation of HMC is its inability to be applied to discrete domains due to the lack of gradient signal. In this work, we introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions using a combination of neural transport methods like normalizing flows and variational dequantization, and the Metropolis-Hastings rule. Our method first learns a continuous embedding of the discrete space using a surjective map and subsequently learns a bijective transformation from the continuous space to an approximately Gaussian distributed latent variable. Sampling proceeds by simulating MCMC chains in the latent space and mapping these samples to the target discrete space via the learned transformations. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.

Didrik Nielsen, Priyank Jaini, Emiel Hoogeboom et al.

Normalizing flows and variational autoencoders are powerful generative models that can represent complicated density functions. However, they both impose constraints on the models: Normalizing flows use bijective transformations to model densities whereas VAEs learn stochastic transformations that are non-invertible and thus typically do not provide tractable estimates of the marginal likelihood. In this paper, we introduce SurVAE Flows: A modular framework of composable transformations that encompasses VAEs and normalizing flows. SurVAE Flows bridge the gap between normalizing flows and VAEs with surjective transformations, wherein the transformations are deterministic in one direction -- thereby allowing exact likelihood computation, and stochastic in the reverse direction -- hence providing a lower bound on the corresponding likelihood. We show that several recently proposed methods, including dequantization and augmented normalizing flows, can be expressed as SurVAE Flows. Finally, we introduce common operations such as the max value, the absolute value, sorting and stochastic permutation as composable layers in SurVAE Flows.

Didrik Nielsen, Ole Winther

Flow models have recently made great progress at modeling ordinal discrete data such as images and audio. Due to the continuous nature of flow models, dequantization is typically applied when using them for such discrete data, resulting in lower bound estimates of the likelihood. In this paper, we introduce subset flows, a class of flows that can tractably transform finite volumes and thus allow exact computation of likelihoods for discrete data. Based on subset flows, we identify ordinal discrete autoregressive models, including WaveNets, PixelCNNs and Transformers, as single-layer flows. We use the flow formulation to compare models trained and evaluated with either the exact likelihood or its dequantization lower bound. Finally, we study multilayer flows composed of PixelCNNs and non-autoregressive coupling layers and demonstrate state-of-the-art results on CIFAR-10 for flow models trained with dequantization.

Aaron Mishkin, Frederik Kunstner, Didrik Nielsen et al.

Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approximation of the covariance matrix despite, the fact that these matrices are known to result in poor uncertainty estimates. To address this issue, we propose a new stochastic, low-rank, approximate natural-gradient (SLANG) method for variational inference in large, deep models. Our method estimates a "diagonal plus low-rank" structure based solely on back-propagated gradients of the network log-likelihood. This requires strictly less gradient computations than methods that compute the gradient of the whole variational objective. Empirical evaluations on standard benchmarks confirm that SLANG enables faster and more accurate estimation of uncertainty than mean-field methods, and performs comparably to state-of-the-art methods.

Mohammad Emtiyaz Khan, Didrik Nielsen

Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating Bayesian inference as an optimization problem and solving it using gradient-based optimization. In this paper, we argue in favor of natural-gradient approaches which, unlike their gradient-based counterparts, can improve convergence by exploiting the information geometry of the solutions. We show how to derive fast yet simple natural-gradient updates by using a duality associated with exponential-family distributions. An attractive feature of these methods is that, by using natural-gradients, they are able to extract accurate local approximations for individual model components. We summarize recent results for Bayesian deep learning showing the superiority of natural-gradient approaches over their gradient counterparts.

Mohammad Emtiyaz Khan, Didrik Nielsen, Voot Tangkaratt et al.

Uncertainty computation in deep learning is essential to design robust and reliable systems. Variational inference (VI) is a promising approach for such computation, but requires more effort to implement and execute compared to maximum-likelihood methods. In this paper, we propose new natural-gradient algorithms to reduce such efforts for Gaussian mean-field VI. Our algorithms can be implemented within the Adam optimizer by perturbing the network weights during gradient evaluations, and uncertainty estimates can be cheaply obtained by using the vector that adapts the learning rate. This requires lower memory, computation, and implementation effort than existing VI methods, while obtaining uncertainty estimates of comparable quality. Our empirical results confirm this and further suggest that the weight-perturbation in our algorithm could be useful for exploration in reinforcement learning and stochastic optimization.

Mohammad Emtiyaz Khan, Wu Lin, Voot Tangkaratt et al.

We present the Variational Adaptive Newton (VAN) method which is a black-box optimization method especially suitable for explorative-learning tasks such as active learning and reinforcement learning. Similar to Bayesian methods, VAN estimates a distribution that can be used for exploration, but requires computations that are similar to continuous optimization methods. Our theoretical contribution reveals that VAN is a second-order method that unifies existing methods in distinct fields of continuous optimization, variational inference, and evolution strategies. Our experimental results show that VAN performs well on a wide-variety of learning tasks. This work presents a general-purpose explorative-learning method that has the potential to improve learning in areas such as active learning and reinforcement learning.