Diffusion models have emerged as a promising class of generative models that map noisy inputs to realistic images. More recently, they have been employed to generate solutions to partial differential equations (PDEs). However, they still struggle with inverse problems in the Laplacian operator, for instance, the Poisson equation, because the eigenvalues that are large in magnitude amplify the measurement noise. This paper presents a novel approach for the inverse and forward solution of PDEs through the use of denoising diffusion restoration models (DDRM). DDRMs were used in linear inverse problems to restore original clean signals by exploiting the singular value decomposition (SVD) of the linear operator. Equivalently, we present an approach to restore the solution and the parameters in the Poisson equation by exploiting the eigenvalues and the eigenfunctions of the Laplacian operator. Our results show that using denoising diffusion restoration significantly improves the estimation of the solution and parameters. Our research, as a result, pioneers the integration of diffusion models with the principles of underlying physics to solve PDEs.
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Diffusion models have recently brought a powerful revolution in image generation. Despite showing impressive generative capabilities, most of these models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. Instead of simply applying moving average to the denoised samples at different timesteps, we first map the denoised samples to data space and then perform moving average to avoid distribution shift across timesteps. In view that diffusion models evolve the recovery from low-frequency components to high-frequency details, we further decompose the samples into different frequency components and execute moving average separately on each component. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)". MASF could be seamlessly integrated into mainstream pre-trained diffusion models and sampling schedules. Extensive experiments on both unconditional and conditional diffusion models demonstrate that our MASF leads to superior performances compared to the baselines, with almost negligible additional complexity cost.
Auto-regressive models have achieved impressive results in 2D image generation by modeling joint distributions in grid space. In this paper, we extend auto-regressive models to 3D domains, and seek a stronger ability of 3D shape generation by improving auto-regressive models at capacity and scalability simultaneously. Firstly, we leverage an ensemble of publicly available 3D datasets to facilitate the training of large-scale models. It consists of a comprehensive collection of approximately 900,000 objects, with multiple properties of meshes, points, voxels, rendered images, and text captions. This diverse labeled dataset, termed Objaverse-Mix, empowers our model to learn from a wide range of object variations. However, directly applying 3D auto-regression encounters critical challenges of high computational demands on volumetric grids and ambiguous auto-regressive order along grid dimensions, resulting in inferior quality of 3D shapes. To this end, we then present a novel framework Argus3D in terms of capacity. Concretely, our approach introduces discrete representation learning based on a latent vector instead of volumetric grids, which not only reduces computational costs but also preserves essential geometric details by learning the joint distributions in a more tractable order. The capacity of conditional generation can thus be realized by simply concatenating various conditioning inputs to the latent vector, such as point clouds, categories, images, and texts. In addition, thanks to the simplicity of our model architecture, we naturally scale up our approach to a larger model with an impressive 3.6 billion parameters, further enhancing the quality of versatile 3D generation. Extensive experiments on four generation tasks demonstrate that Argus3D can synthesize diverse and faithful shapes across multiple categories, achieving remarkable performance.
Diffusion models are just at a tipping point for image super-resolution task. Nevertheless, it is not trivial to capitalize on diffusion models for video super-resolution which necessitates not only the preservation of visual appearance from low-resolution to high-resolution videos, but also the temporal consistency across video frames. In this paper, we propose a novel approach, pursuing Spatial Adaptation and Temporal Coherence (SATeCo), for video super-resolution. SATeCo pivots on learning spatial-temporal guidance from low-resolution videos to calibrate both latent-space high-resolution video denoising and pixel-space video reconstruction. Technically, SATeCo freezes all the parameters of the pre-trained UNet and VAE, and only optimizes two deliberately-designed spatial feature adaptation (SFA) and temporal feature alignment (TFA) modules, in the decoder of UNet and VAE. SFA modulates frame features via adaptively estimating affine parameters for each pixel, guaranteeing pixel-wise guidance for high-resolution frame synthesis. TFA delves into feature interaction within a 3D local window (tubelet) through self-attention, and executes cross-attention between tubelet and its low-resolution counterpart to guide temporal feature alignment. Extensive experiments conducted on the REDS4 and Vid4 datasets demonstrate the effectiveness of our approach.
In image restoration (IR), leveraging semantic priors from segmentation models has been a common approach to improve performance. The recent segment anything model (SAM) has emerged as a powerful tool for extracting advanced semantic priors to enhance IR tasks. However, the computational cost of SAM is prohibitive for IR, compared to existing smaller IR models. The incorporation of SAM for extracting semantic priors considerably hampers the model inference efficiency. To address this issue, we propose a general framework to distill SAM's semantic knowledge to boost exiting IR models without interfering with their inference process. Specifically, our proposed framework consists of the semantic priors fusion (SPF) scheme and the semantic priors distillation (SPD) scheme. SPF fuses two kinds of information between the restored image predicted by the original IR model and the semantic mask predicted by SAM for the refined restored image. SPD leverages a self-distillation manner to distill the fused semantic priors to boost the performance of original IR models. Additionally, we design a semantic-guided relation (SGR) module for SPD, which ensures semantic feature representation space consistency to fully distill the priors. We demonstrate the effectiveness of our framework across multiple IR models and tasks, including deraining, deblurring, and denoising.
Stress models are a promising approach for graph drawing. They minimize the weighted sum of the squared errors of the Euclidean and desired distances for each node pair. The desired distance typically uses the graph-theoretic distances obtained from the all-node pair shortest path problem. In a minimized stress function, the obtained coordinates are affected by the non-Euclidean property and the high-dimensionality of the graph-theoretic distance matrix. Therefore, the graph-theoretic distances used in stress models may not necessarily be the best metric for determining the node coordinates. In this study, we propose two different methods of adjusting the graph-theoretical distance matrix to a distance matrix suitable for graph drawing while preserving its structure. The first method is the application of eigenvalue decomposition to the inner product matrix obtained from the distance matrix and the obtainment of a new distance matrix by setting some eigenvalues with small absolute values to zero. The second approach is the usage of a stress model modified by adding a term that minimizes the Frobenius norm between the adjusted and original distance matrices. We perform computational experiments using several benchmark graphs to demonstrate that the proposed method improves some quality metrics, including the node resolution and the Gabriel graph property, when compared to conventional stress models.
People grasp flexible visual concepts from a few examples. We explore a neurosymbolic system that learns how to infer programs that capture visual concepts in a domain-general fashion. We introduce Template Programs: programmatic expressions from a domain-specific language that specify structural and parametric patterns common to an input concept. Our framework supports multiple concept-related tasks, including few-shot generation and co-segmentation through parsing. We develop a learning paradigm that allows us to train networks that infer Template Programs directly from visual datasets that contain concept groupings. We run experiments across multiple visual domains: 2D layouts, Omniglot characters, and 3D shapes. We find that our method outperforms task-specific alternatives, and performs competitively against domain-specific approaches for the limited domains where they exist.
Existing knowledge graph (KG) embedding models have primarily focused on static KGs. However, real-world KGs do not remain static, but rather evolve and grow in tandem with the development of KG applications. Consequently, new facts and previously unseen entities and relations continually emerge, necessitating an embedding model that can quickly learn and transfer new knowledge through growth. Motivated by this, we delve into an expanding field of KG embedding in this paper, i.e., lifelong KG embedding. We consider knowledge transfer and retention of the learning on growing snapshots of a KG without having to learn embeddings from scratch. The proposed model includes a masked KG autoencoder for embedding learning and update, with an embedding transfer strategy to inject the learned knowledge into the new entity and relation embeddings, and an embedding regularization method to avoid catastrophic forgetting. To investigate the impacts of different aspects of KG growth, we construct four datasets to evaluate the performance of lifelong KG embedding. Experimental results show that the proposed model outperforms the state-of-the-art inductive and lifelong embedding baselines.
Answering questions that require reading texts in an image is challenging for current models. One key difficulty of this task is that rare, polysemous, and ambiguous words frequently appear in images, e.g., names of places, products, and sports teams. To overcome this difficulty, only resorting to pre-trained word embedding models is far from enough. A desired model should utilize the rich information in multiple modalities of the image to help understand the meaning of scene texts, e.g., the prominent text on a bottle is most likely to be the brand. Following this idea, we propose a novel VQA approach, Multi-Modal Graph Neural Network (MM-GNN). It first represents an image as a graph consisting of three sub-graphs, depicting visual, semantic, and numeric modalities respectively. Then, we introduce three aggregators which guide the message passing from one graph to another to utilize the contexts in various modalities, so as to refine the features of nodes. The updated nodes have better features for the downstream question answering module. Experimental evaluations show that our MM-GNN represents the scene texts better and obviously facilitates the performances on two VQA tasks that require reading scene texts.
Visual Question Answering (VQA) models have struggled with counting objects in natural images so far. We identify a fundamental problem due to soft attention in these models as a cause. To circumvent this problem, we propose a neural network component that allows robust counting from object proposals. Experiments on a toy task show the effectiveness of this component and we obtain state-of-the-art accuracy on the number category of the VQA v2 dataset without negatively affecting other categories, even outperforming ensemble models with our single model. On a difficult balanced pair metric, the component gives a substantial improvement in counting over a strong baseline by 6.6%.
Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree of over-segmentation produced. It still remains a challenge to properly select such parameters for human-like perceptual grouping. In this work, we exploit the diversity of segments produced by different choices of parameters. We scan the segmentation parameter space and generate a collection of image segmentation hypotheses (from highly over-segmented to under-segmented). These are fed into a cost minimization framework that produces the final segmentation by selecting segments that: (1) better describe the natural contours of the image, and (2) are more stable and persistent among all the segmentation hypotheses. We compare our algorithm's performance with state-of-the-art algorithms, showing that we can achieve improved results. We also show that our framework is robust to the choice of segmentation kernel that produces the initial set of hypotheses.
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