Offline black-box optimization aims to maximize a black-box function using an offline dataset of designs and their measured properties. Two main approaches have emerged: the forward approach, which learns a mapping from input to its value, thereby acting as a proxy to guide optimization, and the inverse approach, which learns a mapping from value to input for conditional generation. (a) Although proxy-free~(classifier-free) diffusion shows promise in robustly modeling the inverse mapping, it lacks explicit guidance from proxies, essential for generating high-performance samples beyond the training distribution. Therefore, we propose \textit{proxy-enhanced sampling} which utilizes the explicit guidance from a trained proxy to bolster proxy-free diffusion with enhanced sampling control. (b) Yet, the trained proxy is susceptible to out-of-distribution issues. To address this, we devise the module \textit{diffusion-based proxy refinement}, which seamlessly integrates insights from proxy-free diffusion back into the proxy for refinement. To sum up, we propose \textit{\textbf{R}obust \textbf{G}uided \textbf{D}iffusion for Offline Black-box Optimization}~(\textbf{RGD}), combining the advantages of proxy~(explicit guidance) and proxy-free diffusion~(robustness) for effective conditional generation. RGD achieves state-of-the-art results on various design-bench tasks, underscoring its efficacy. Our code is at https://github.com/GGchen1997/RGD.

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g. Euclidean, limiting their applications to many domains where the data has a functional form such as in scientific computing and 3D geometric data analysis. In this work, we introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. In DDOs, the forward process perturbs input functions gradually using a Gaussian process. The generative process is formulated by integrating a function-valued Langevin dynamic. Our approach requires an appropriate notion of the score for the perturbed data distribution, which we obtain by generalizing denoising score matching to function spaces that can be infinite-dimensional. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost that is independent of the data resolution. We theoretically and numerically verify the applicability of our approach on a set of problems, including generating solutions to the Navier-Stokes equation viewed as the push-forward distribution of forcings from a Gaussian Random Field (GRF).

In this work we theoretically show that conservative objective models (COMs) for offline model-based optimisation (MBO) are a special kind of contrastive divergence-based energy model, one where the energy function represents both the unconditional probability of the input and the conditional probability of the reward variable. While the initial formulation only samples modes from its learned distribution, we propose a simple fix that replaces its gradient ascent sampler with a Langevin MCMC sampler. This gives rise to a special probabilistic model where the probability of sampling an input is proportional to its predicted reward. Lastly, we show that better samples can be obtained if the model is decoupled so that the unconditional and conditional probabilities are modelled separately.

In offline model-based optimisation (MBO) we are interested in using machine learning to design candidates that maximise some measure of desirability through an expensive but real-world scoring process. Offline MBO tries to approximate this expensive scoring function and use that to evaluate generated designs, however evaluation is non-exact because one approximation is being evaluated with another. Instead, we ask ourselves: if we did have the real world scoring function at hand, what cheap-to-compute validation metrics would correlate best with this? Since the real-world scoring function is available for simulated MBO datasets, insights obtained from this can be transferred over to real-world offline MBO tasks where the real-world scoring function is expensive to compute. To address this, we propose a conceptual evaluation framework that is amenable to measuring extrapolation, and apply this to conditional denoising diffusion models. Empirically, we find that two validation metrics -- agreement and Frechet distance -- correlate quite well with the ground truth. When there is high variability in conditional generation, feedback is required in the form of an approximated version of the real-world scoring function. Furthermore, we find that generating high-scoring samples may require heavily weighting the generative model in favour of sample quality, potentially at the cost of sample diversity.

Different types of mental rotation tests have been used extensively in psychology to understand human visual reasoning and perception. Understanding what an object or visual scene would look like from another viewpoint is a challenging problem that is made even harder if it must be performed from a single image. We explore a controlled setting whereby questions are posed about the properties of a scene if that scene was observed from another viewpoint. To do this we have created a new version of the CLEVR dataset that we call CLEVR Mental Rotation Tests (CLEVR-MRT). Using CLEVR-MRT we examine standard methods, show how they fall short, then explore novel neural architectures that involve inferring volumetric representations of a scene. These volumes can be manipulated via camera-conditioned transformations to answer the question. We examine the efficacy of different model variants through rigorous ablations and demonstrate the efficacy of volumetric representations.

Then detection and identification of extreme weather events in large-scale climate simulations is an important problem for risk management, informing governmental policy decisions and advancing our basic understanding of the climate system. Recent work has shown that fully supervised convolutional neural networks (CNNs) can yield acceptable accuracy for classifying well-known types of extreme weather events when large amounts of labeled data are available. However, many different types of spatially localized climate patterns are of interest including hurricanes, extra-tropical cyclones, weather fronts, and blocking events among others. Existing labeled data for these patterns can be incomplete in various ways, such as covering only certain years or geographic areas and having false negatives. This type of climate data therefore poses a number of interesting machine learning challenges.

In this paper, we explore new approaches to combining information encoded within the learned representations of autoencoders. We explore models that are capable of combining the attributes of multiple inputs such that a resynthesised output is trained to fool an adversarial discriminator for real versus synthesised data. Furthermore, we explore the use of such an architecture in the context of semi-supervised learning, where we learn a mixing function whose objective is to produce interpolations of hidden states, or masked combinations of latent representations that are consistent with a conditioned class label. We show quantitative and qualitative evidence that such a formulation is an interesting avenue of research. The autoencoder is a fundamental building block in unsupervised learning. Autoencoders are trained to reconstruct their inputs after being processed by two neural networks: an encoder which encodes the input to a high-level representation or bottleneck, and a decoder which performs the reconstruction using the representation as input.

We present an unsupervised approach for learning to estimate three dimensional (3D) facial structure from a single image while also predicting 3D viewpoint transformations that match a desired pose and facial geometry. We achieve this by inferring the depth of facial keypoints of an input image in an unsupervised manner, without using any form of ground-truth depth information. We show how it is possible to use these depths as intermediate computations within a new backpropable loss to predict the parameters of a 3D affine transformation matrix that maps inferred 3D keypoints of an input face to the corresponding 2D keypoints on a desired target facial geometry or pose. Our resulting approach, called DepthNets, can therefore be used to infer plausible 3D transformations from one face pose to another, allowing faces to be frontalized, transformed into 3D models or even warped to another pose and facial geometry. Lastly, we identify certain shortcomings with our formulation, and explore adversarial image translation techniques as a post-processing step to re-synthesize complete head shots for faces re-targeted to different poses or identities.

We present an unsupervised approach for learning to estimate three dimensional (3D) facial structure from a single image while also predicting 3D viewpoint transformations that match a desired pose and facial geometry. We achieve this by inferring the depth of facial keypoints of an input image in an unsupervised manner, without using any form of ground-truth depth information. We show how it is possible to use these depths as intermediate computations within a new backpropable loss to predict the parameters of a 3D affine transformation matrix that maps inferred 3D keypoints of an input face to the corresponding 2D keypoints on a desired target facial geometry or pose. Our resulting approach, called DepthNets, can therefore be used to infer plausible 3D transformations from one face pose to another, allowing faces to be frontalized, transformed into 3D models or even warped to another pose and facial geometry. Lastly, we identify certain shortcomings with our formulation, and explore adversarial image translation techniques as a post-processing step to re-synthesize complete head shots for faces re-targeted to different poses or identities.

Deep networks often perform well on the data manifold on which they are trained, yet give incorrect (and often very confident) answers when evaluated on points from off of the training distribution. This is exemplified by the adversarial examples phenomenon but can also be seen in terms of model generalization and domain shift. We propose Manifold Mixup which encourages the network to produce more reasonable and less confident predictions at points with combinations of attributes not seen in the training set. This is accomplished by training on convex combinations of the hidden state representations of data samples. Using this method, we demonstrate improved semi-supervised learning, learning with limited labeled data, and robustness to adversarial examples. Manifold Mixup requires no (significant) additional computation. Analytical experiments on both real data and synthetic data directly support our hypothesis for why the Manifold Mixup method improves results.