Gurprit Singh

Corentin Salaün, Xingchang Huang, Iliyan Georgiev et al.

We introduce a theoretical and practical framework for efficient importance sampling of mini-batch samples for gradient estimation from single and multiple probability distributions. To handle noisy gradients, our framework dynamically evolves the importance distribution during training by utilizing a self-adaptive metric. Our framework combines multiple, diverse sampling distributions, each tailored to specific parameter gradients. This approach facilitates the importance sampling of vector-valued gradient estimation. Rather than naively combining multiple distributions, our framework involves optimally weighting data contribution across multiple distributions. This adapted combination of multiple importance yields superior gradient estimates, leading to faster training convergence. We demonstrate the effectiveness of our approach through empirical evaluations across a range of optimization tasks like classification and regression on both image and point cloud datasets.

Corentin Salaün, Xingchang Huang, Iliyan Georgiev et al.

Machine learning optimization often depends on stochastic gradient descent, where the precision of gradient estimation is vital for model performance. Gradients are calculated from mini-batches formed by uniformly selecting data samples from the training dataset. However, not all data samples contribute equally to gradient estimation. To address this, various importance sampling strategies have been developed to prioritize more significant samples. Despite these advancements, all current importance sampling methods encounter challenges related to computational efficiency and seamless integration into practical machine learning pipelines. In this work, we propose a practical algorithm that efficiently computes data importance on-the-fly during training, eliminating the need for dataset preprocessing. We also introduce a novel metric based on the derivative of the loss w.r.t. the network output, designed for mini-batch importance sampling. Our metric prioritizes influential data points, thereby enhancing gradient estimation accuracy. We demonstrate the effectiveness of our approach across various applications. We first perform classification and regression tasks to demonstrate improvements in accuracy. Then, we show how our approach can also be used for online data pruning by identifying and discarding data samples that contribute minimally towards the training loss. This significantly reduce training time with negligible loss in the accuracy of the model.

Martin Balint, Karol Myszkowski, Hans-Peter Seidel et al.

When dealing with difficult inverse problems such as inverse rendering, using Monte Carlo estimated gradients to optimise parameters can slow down convergence due to variance. Averaging many gradient samples in each iteration reduces this variance trivially. However, for problems that require thousands of optimisation iterations, the computational cost of this approach rises quickly. We derive a theoretical framework for interleaving sampling and optimisation. We update and reuse past samples with low-variance finite-difference estimators that describe the change in the estimated gradients between each iteration. By combining proportional and finite-difference samples, we continuously reduce the variance of our novel gradient meta-estimators throughout the optimisation process. We investigate how our estimator interlinks with Adam and derive a stable combination. We implement our method for inverse path tracing and demonstrate how our estimator speeds up convergence on difficult optimisation tasks.

Shishir Reddy Vutukur, Mengkejiergeli Ba, Benjamin Busam et al.

In this paper, we propose a novel encoder-decoder architecture, named SABER, to learn the 6D pose of the object in the embedding space by learning shape representation at a given pose. This model enables us to learn pose by performing shape representation at a target pose from RGB image input. We perform shape representation as an auxiliary task which helps us in learning rotations space for an object based on 2D images. An image encoder predicts the rotation in the embedding space and the DeepSDF based decoder learns to represent the object's shape at the given pose. As our approach is shape based, the pipeline is suitable for any type of object irrespective of the symmetry. Moreover, we need only a CAD model of the objects to train SABER. Our pipeline is synthetic data based and can also handle symmetric objects without symmetry labels and, thus, no additional labeled training data is needed. The experimental evaluation shows that our method achieves close to benchmark results for both symmetric objects and asymmetric objects on Occlusion-LineMOD, and T-LESS datasets.

Jente Vandersanden, Sascha Holl, Xingchang Huang et al.

Classical diffusion models typically rely on isotropic Gaussian noise, treating all regions uniformly and overlooking structural information important for high-quality generation. We introduce an edge-preserving diffusion process that generalizes isotropic models via a hybrid noise scheme with an edge-aware scheduler that smoothly transitions from edge-preserving to isotropic noise. This enables the model to capture fine structural details while generally maintaining global performance. We evaluate the impact of structure-aware noise in both diffusion and flow-matching frameworks, and show that existing isotropic models can be efficiently fine-tuned with edge-preserving noise, making our framework practical for adapting pre-trained systems. Beyond unconditional generation, our method particularly shows improvements in structure-guided tasks such as stroke-to-image synthesis, improving robustness and perceptual quality, as evidenced by consistent improvements across FID, KID, and CLIP-score.

Sascha Holl, Gurprit Singh, Hans-Peter Seidel

We present Diffusion Restore, a real-time framework for diffusion-based MCMC light transport. MCMC methods are highly suitable for sampling from complex high-dimensional distributions and for approximating integrals over them. In practice, they are often the only viable solution when direct sampling is not possible and alternative methods are either inefficient or cannot be applied due to the structure of the target distribution. However, controlling the exploration of the target distribution in MCMC methods remains challenging. Efficient exploration requires a balance between local exploration and global discovery, and local dynamics must rapidly explore individual modes without getting stuck or exhibiting excessive backtracking. The problem of global discovery has recently been addressed by the introduction of the Restore framework. In this work, we build on this framework and focus on improving local exploration. We show how to choose diffusion-based local dynamics within the Restore framework while completely avoiding Metropolis-adjustment, which is known to slow down convergence. Furthermore, we model these dynamics as nonreversible, introducing momentum in the drift and thereby enabling more directed exploration of the target distribution compared to reversible, random-walk-like dynamics. We provide a theoretical justification for the validity of our choice of local dynamics. Empirically, we demonstrate across diverse scenes that Diffusion Restore outperforms all existing MCMC light transport methods and establishes a new state of the art. In addition, we present a GPU implementation in ray tracing and compute shaders and achieve real-time frame rates. This demonstrates that Diffusion Restore is not only superior in offline rendering, but also outperforms traditional Path Tracing methods in real-time rendering settings, such as interactive applications and games.

Sascha Holl, Jente Vandersanden, Gurprit Singh et al.

Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images being highly dependent on the design of the forward (diffusion) process. Among these, models based on stochastic differential equations (SDEs) have proven particularly effective. While traditional methods aim to progressively destroy all image information to enable reconstruction from pure noise, we propose a class of anisotropic stochastic partial differential equations (SPDEs) that preserve the geometric structure of the data over longer time scales throughout the transformation. These SPDEs consist of a drift term that enforces deterministic destruction via structured smoothing, and a diffusion coefficient that enables random destruction through noise injection. Both components are governed by anisotropy coefficients, enabling controlled, direction-dependent information degradation. This framework provides the theoretical foundation for a novel anisotropic score-based generative model. By retaining geometric structure for longer time scales, the backward generative process can exploit residual geometric cues, leading to improved reconstruction fidelity. We empirically validate this improvement in a proof-of-concept implementation on unconditional image generation, showing that anisotropic diffusion can achieve superior image quality metrics. We demonstrate consistent improvements in both pixel and latent space experiments over the SDE-driven baseline as well as over the state-of-the-art Flow Matching approach. Finally, we demonstrate the effectiveness of the introduced anisotropy in a conditional stroke-to-image generation task.

Sascha Holl, Gurprit Singh, Hans-Peter Seidel

In light transport simulation, Markov chain Monte Carlo methods are particularly effective at exploring regions with complex lighting characteristics. However, estimator variance is a central concern across Monte Carlo methods in general. In light transport, high variance directly manifests as increased noise or, equivalently, longer rendering times at fixed image quality. Variance reduction techniques based on Rao-Blackwellization have proven particularly effective. In practice, however, the RB approach traditionally used in light transport, waste-recycling, can yield little to no measurable variance reduction, a fact we empirically confirm in this work. Motivated by this lack of effective variance reduction, we introduce a novel RB technique for the general-purpose Metropolis-Hastings algorithm that is computationally efficient and achieves substantial variance reduction. We show that this method consistently outperforms waste-recycling in terms of both variance reduction and convergence speed. Building on this result, we adapt the proposed RB approach to the recently introduced general-purpose Jump Restore algorithm, where it similarly achieves substantial variance reduction and accelerated convergence. Through extensive experiments in light transport simulation, we demonstrate that our \gls{rb} technique significantly outperforms the traditional approaches for both MH-based light transport algorithms and Jump Restore Light Transport, under both equal-time and equal-sample-count comparisons.

Xingchang Huang, Corentin Salaün, Cristina Vasconcelos et al.

Most of the existing diffusion models use Gaussian noise for training and sampling across all time steps, which may not optimally account for the frequency contents reconstructed by the denoising network. Despite the diverse applications of correlated noise in computer graphics, its potential for improving the training process has been underexplored. In this paper, we introduce a novel and general class of diffusion models taking correlated noise within and across images into account. More specifically, we propose a time-varying noise model to incorporate correlated noise into the training process, as well as a method for fast generation of correlated noise mask. Our model is built upon deterministic diffusion models and utilizes blue noise to help improve the generation quality compared to using Gaussian white (random) noise only. Further, our framework allows introducing correlation across images within a single mini-batch to improve gradient flow. We perform both qualitative and quantitative evaluations on a variety of datasets using our method, achieving improvements on different tasks over existing deterministic diffusion models in terms of FID metric.

Gurprit Singh, Wenzel Jakob

Generative artificial intelligence (AI) has made unprecedented advances in vision language models over the past two years. During the generative process, new samples (images) are generated from an unknown high-dimensional distribution. Markov Chain Monte Carlo (MCMC) methods are particularly effective in drawing samples from such complex, high-dimensional distributions. This makes MCMC methods an integral component for models like EBMs, ensuring accurate sample generation. Gradient-based optimization is at the core of modern generative models. The update step during the optimization forms a Markov chain where the new update depends only on the current state. This allows exploration of the parameter space in a memoryless manner, thus combining the benefits of gradient-based optimization and MCMC sampling. MCMC methods have shown an equally important role in physically based rendering where complex light paths are otherwise quite challenging to sample from simple importance sampling techniques. A lot of research is dedicated towards bringing physical realism to samples (images) generated from diffusion-based generative models in a data-driven manner, however, a unified framework connecting these techniques is still missing. In this course, we take the first steps toward understanding each of these components and exploring how MCMC could potentially serve as a bridge, linking these closely related areas of research. Our course aims to provide necessary theoretical and practical tools to guide students, researchers and practitioners towards the common goal of generative physically based rendering. All Jupyter notebooks with demonstrations associated to this tutorial can be found on the project webpage: https://sinbag.github.io/mcmc/

Quan Zheng, Gurprit Singh, Hans-Peter Seidel

Learning neural radiance fields of a scene has recently allowed realistic novel view synthesis of the scene, but they are limited to synthesize images under the original fixed lighting condition. Therefore, they are not flexible for the eagerly desired tasks like relighting, scene editing and scene composition. To tackle this problem, several recent methods propose to disentangle reflectance and illumination from the radiance field. These methods can cope with solid objects with opaque surfaces but participating media are neglected. Also, they take into account only direct illumination or at most one-bounce indirect illumination, thus suffer from energy loss due to ignoring the high-order indirect illumination. We propose to learn neural representations for participating media with a complete simulation of global illumination. We estimate direct illumination via ray tracing and compute indirect illumination with spherical harmonics. Our approach avoids computing the lengthy indirect bounces and does not suffer from energy loss. Our experiments on multiple scenes show that our approach achieves superior visual quality and numerical performance compared to state-of-the-art methods, and it can generalize to deal with solid objects with opaque surfaces as well.

Yifan Xu, Tianqi Fan, Yi Yuan et al.

Deep implicit field regression methods are effective for 3D reconstruction from single-view images. However, the impact of different sampling patterns on the reconstruction quality is not well-understood. In this work, we first study the effect of point set discrepancy on the network training. Based on Farthest Point Sampling algorithm, we propose a sampling scheme that theoretically encourages better generalization performance, and results in fast convergence for SGD-based optimization algorithms. Secondly, based on the reflective symmetry of an object, we propose a feature fusion method that alleviates issues due to self-occlusions which makes it difficult to utilize local image features. Our proposed system Ladybird is able to create high quality 3D object reconstructions from a single input image. We evaluate Ladybird on a large scale 3D dataset (ShapeNet) demonstrating highly competitive results in terms of Chamfer distance, Earth Mover's distance and Intersection Over Union (IoU).