Marcin Mazur

Ignacy Kolton, Kacper Marzol, Paweł Batorski et al.

Machine unlearning is a key defense mechanism for removing unauthorized concepts from text-to-image diffusion models, yet recent evidence shows that latent visual information often persists after unlearning. Existing adversarial approaches for exploiting this leakage are constrained by fundamental limitations: optimization-based methods are computationally expensive due to per-instance iterative search. At the same time, reasoning-based and heuristic techniques lack direct feedback from the target model's latent visual representations. To address these challenges, we introduce ReLAPSe, a policy-based adversarial framework that reformulates concept restoration as a reinforcement learning problem. ReLAPSe trains an agent using Reinforcement Learning with Verifiable Rewards (RLVR), leveraging the diffusion model's noise prediction loss as a model-intrinsic and verifiable feedback signal. This closed-loop design directly aligns textual prompt manipulation with latent visual residuals, enabling the agent to learn transferable restoration strategies rather than optimizing isolated prompts. By pioneering the shift from per-instance optimization to global policy learning, ReLAPSe achieves efficient, near-real-time recovery of fine-grained identities and styles across multiple state-of-the-art unlearning methods, providing a scalable tool for rigorous red-teaming of unlearned diffusion models. Some experimental evaluations involve sensitive visual concepts, such as nudity. Code is available at https://github.com/gmum/ReLaPSe

Matteo Nulli, Vladimir Orshulevich, Tala Bazazo et al.

E-commerce product understanding demands by nature, strong multimodal comprehension from text, images, and structured attributes. General-purpose Vision-Language Models (VLMs) enable generalizable multimodal latent modelling, yet there is no documented, well-known strategy for adapting them to the attribute-centric, multi-image, and noisy nature of e-commerce data, without sacrificing general performance. In this work, we show through a large-scale experimental study, how targeted adaptation of general VLMs can substantially improve e-commerce performance while preserving broad multimodal capabilities. Furthermore, we propose a novel extensive evaluation suite covering deep product understanding, strict instruction following, and dynamic attribute extraction.

Piotr Borycki, Weronika Smolak, Joanna Waczyńska et al.

Physics simulation is paramount for modeling and utilizing 3D scenes in various real-world applications. However, integrating with state-of-the-art 3D scene rendering techniques such as Gaussian Splatting (GS) remains challenging. Existing models use additional meshing mechanisms, including triangle or tetrahedron meshing, marching cubes, or cage meshes. Alternatively, we can modify the physics-grounded Newtonian dynamics to align with 3D Gaussian components. Current models take the first-order approximation of a deformation map, which locally approximates the dynamics by linear transformations. In contrast, our GS for Physics-Based Simulations (GASP) pipeline uses parametrized flat Gaussian distributions. Consequently, the problem of modeling Gaussian components using the physics engine is reduced to working with 3D points. In our work, we present additional rules for manipulating Gaussians, demonstrating how to adapt the pipeline to incorporate meshes, control Gaussian sizes during simulations, and enhance simulation efficiency. This is achieved through the Gaussian grouping strategy, which implements hierarchical structuring and enables simulations to be performed exclusively on selected Gaussians. The resulting solution can be integrated into any physics engine that can be treated as a black box. As demonstrated in our studies, the proposed pipeline exhibits superior performance on a diverse range of benchmark datasets designed for 3D object rendering. The project webpage, which includes additional visualizations, can be found at https://waczjoan.github.io/GASP.

Łukasz Struski, Marcin Mazur, Paweł Batorski et al.

Many crucial problems in deep learning and statistical inference are caused by a variational gap, i.e., a difference between model evidence (log-likelihood) and evidence lower bound (ELBO). In particular, in a classical VAE setting that involves training via an ELBO cost function, it is difficult to provide a robust comparison of the effects of training between models, since we do not know a log-likelihood of data (but only its lower bound). In this paper, to deal with this problem, we introduce a general and effective upper bound, which allows us to efficiently approximate the evidence of data. We provide extensive theoretical and experimental studies of our approach, including its comparison to the other state-of-the-art upper bounds, as well as its application as a tool for the evaluation of models that were trained on various lower bounds.

Adam Kania, Artur Kasymov, Jakub Kościukiewicz et al.

The recent surge in popularity of deep generative models for 3D objects has highlighted the need for more efficient training methods, particularly given the difficulties associated with training with conventional 3D representations, such as voxels or point clouds. Neural Radiance Fields (NeRFs), which provide the current benchmark in terms of quality for the generation of novel views of complex 3D scenes from a limited set of 2D images, represent a promising solution to this challenge. However, the training of these models requires the knowledge of the respective camera positions from which the images were viewed. In this paper, we overcome this limitation by introducing HyperNeRFGAN, a Generative Adversarial Network (GAN) architecture employing a hypernetwork paradigm to transform a Gaussian noise into the weights of a NeRF architecture that does not utilize viewing directions in its training phase. Consequently, as evidenced by the findings of our experimental study, the proposed model, despite its notable simplicity in comparison to existing state-of-the-art alternatives, demonstrates superior performance on a diverse range of image datasets where camera position estimation is challenging, particularly in the context of medical data.

Jakub Stępień, Marcin Mazur, Jacek Tabor et al.

Sparse Autoencoders (SAEs) have become an important tool in mechanistic interpretability, helping to analyze internal representations in both Large Language Models (LLMs) and Vision Transformers (ViTs). By decomposing polysemantic activations into sparse sets of monosemantic features, SAEs aim to translate neural network computations into human-understandable concepts. However, common architectures such as TopK SAEs rely on a fixed sparsity level. They enforce the same number of active features (K) across all inputs, ignoring the varying complexity of real-world data. Natural data often lies on manifolds with varying local intrinsic dimensionality, meaning the number of relevant factors can change significantly across samples. This suggests that a fixed sparsity level is not optimal. Simple inputs may require only a few features, while more complex ones need more expressive representations. Using a constant K can therefore introduce noise in simple cases or miss important structure in more complex ones. To address this issue, we propose SoftSAE, a sparse autoencoder with a Dynamic Top-K selection mechanism. Our method uses a differentiable Soft Top-K operator to learn an input-dependent sparsity level k. This allows the model to adjust the number of active features based on the complexity of each input. As a result, the representation better matches the structure of the data, and the explanation length reflects the amount of information in the input. Experimental results confirm that SoftSAE not only finds meaningful features, but also selects the right number of features for each concept. The source code is available at: https://anonymous.4open.science/r/SoftSAE-8F71/.

Weronika Smolak-Dyżewska, Dawid Malarz, Kornel Howil et al.

Implicit Neural Representations (INRs) employ neural networks to approximate discrete data as continuous functions. In the context of video data, such models can be utilized to transform the coordinates of pixel locations along with frame occurrence times (or indices) into RGB color values. Although INRs facilitate effective compression, they are unsuitable for editing purposes. One potential solution is to use a 3D Gaussian Splatting (3DGS) based model, such as the Video Gaussian Representation (VGR), which is capable of encoding video as a multitude of 3D Gaussians and is applicable for numerous video processing operations, including editing. Nevertheless, in this case, the capacity for modification is constrained to a limited set of basic transformations. To address this issue, we introduce the Video Gaussian Splatting (VeGaS) model, which enables realistic modifications of video data. To construct VeGaS, we propose a novel family of Folded-Gaussian distributions designed to capture nonlinear dynamics in a video stream and model consecutive frames by 2D Gaussians obtained as respective conditional distributions. Our experiments demonstrate that VeGaS outperforms state-of-the-art solutions in frame reconstruction tasks and allows realistic modifications of video data. The code is available at: https://github.com/gmum/VeGaS.

Grzegorz Wilczyński, Rafał Tobiasz, Paweł Gora et al.

Recent advances in neural rendering, particularly 3D Gaussian Splatting (3DGS), have enabled real-time rendering of complex scenes. However, standard 3DGS relies on spherical harmonics, which often struggle to accurately capture high-frequency view-dependent effects such as sharp reflections and transparency. While hybrid approaches like Viewing Direction Gaussian Splatting (VDGS) mitigate this limitation using classical Multi-Layer Perceptrons (MLPs), they remain limited by the expressivity of classical networks in low-parameter regimes. In this paper, we introduce QuantumGS, a novel hybrid framework that integrates Variational Quantum Circuits (VQC) into the Gaussian Splatting pipeline. We propose a unique encoding strategy that maps the viewing direction directly onto the Bloch sphere, leveraging the natural geometry of qubits to represent 3D directional data. By replacing classical color-modulating networks with quantum circuits generated via a hypernetwork or conditioning mechanism, we achieve higher expressivity and better generalization. Source code is available in the supplementary material. Code is available at https://github.com/gwilczynski95/QuantumGS

Rafał Tobiasz, Grzegorz Wilczyński, Marcin Mazur et al.

Gaussian Splatting (GS) is a recent and pivotal technique in 3D computer graphics. GS-based algorithms almost always bypass classical methods such as ray tracing, which offers numerous inherent advantages for rendering. For example, ray tracing is able to handle incoherent rays for advanced lighting effects, including shadows and reflections. To address this limitation, we introduce MeshSplats, a method which converts GS to a mesh-like format. Following the completion of training, MeshSplats transforms Gaussian elements into mesh faces, enabling rendering using ray tracing methods with all their associated benefits. Our model can be utilized immediately following transformation, yielding a mesh of slightly reduced quality without additional training. Furthermore, we can enhance the reconstruction quality through the application of a dedicated optimization algorithm that operates on mesh faces rather than Gaussian components. The efficacy of our method is substantiated by experimental results, underscoring its extensive applications in computer graphics and image processing.

Krzysztof Byrski, Marcin Mazur, Jacek Tabor et al.

3D Gaussian Splatting (3DGS) is a process that enables the direct creation of 3D objects from 2D images. This representation offers numerous advantages, including rapid training and rendering. However, a significant limitation of 3DGS is the challenge of incorporating light and shadow reflections, primarily due to the utilization of rasterization rather than ray tracing for rendering. This paper introduces RaySplats, a model that employs ray-tracing based Gaussian Splatting. Rather than utilizing the projection of Gaussians, our method employs a ray-tracing mechanism, operating directly on Gaussian primitives represented by confidence ellipses with RGB colors. In practice, we compute the intersection between ellipses and rays to construct ray-tracing algorithms, facilitating the incorporation of meshes with Gaussian Splatting models and the addition of lights, shadows, and other related effects.

Paweł Batorski, Dawid Malarz, Marcin Przewięźlikowski et al.

Neural radiance fields (NeRFs) are a widely accepted standard for synthesizing new 3D object views from a small number of base images. However, NeRFs have limited generalization properties, which means that we need to use significant computational resources to train individual architectures for each item we want to represent. To address this issue, we propose a few-shot learning approach based on the hypernetwork paradigm that does not require gradient optimization during inference. The hypernetwork gathers information from the training data and generates an update for universal weights. As a result, we have developed an efficient method for generating a high-quality 3D object representation from a small number of images in a single step. This has been confirmed by direct comparison with the state-of-the-art solutions and a comprehensive ablation study.

Agnieszka Polowczyk, Alicja Polowczyk, Dawid Malarz et al.

Recent advances in large-scale text-to-image diffusion models have heightened concerns about their potential misuse, especially in generating harmful or misleading content. This underscores the urgent need for effective machine unlearning, i.e., removing specific knowledge or concepts from pretrained models without compromising overall performance. One possible approach is Low-Rank Adaptation (LoRA), which offers an efficient means to fine-tune models for targeted unlearning. However, LoRA often inadvertently alters unrelated content, leading to diminished image fidelity and realism. To address this limitation, we introduce UnGuide -- a novel approach which incorporates UnGuidance, a dynamic inference mechanism that leverages Classifier-Free Guidance (CFG) to exert precise control over the unlearning process. UnGuide modulates the guidance scale based on the stability of a few first steps of denoising processes, enabling selective unlearning by LoRA adapter. For prompts containing the erased concept, the LoRA module predominates and is counterbalanced by the base model; for unrelated prompts, the base model governs generation, preserving content fidelity. Empirical results demonstrate that UnGuide achieves controlled concept removal and retains the expressive power of diffusion models, outperforming existing LoRA-based methods in both object erasure and explicit content removal tasks.

Kacper Marzol, Ignacy Kolton, Weronika Smolak-Dyżewska et al.

Multi-modal three-dimensional (3D) medical imaging data, derived from ultrasound, magnetic resonance imaging (MRI), and potentially computed tomography (CT), provide a widely adopted approach for non-invasive anatomical visualization. Accurate modeling, registration, and visualization in this setting depend on surface reconstruction and frame-to-frame interpolation. Traditional methods often face limitations due to image noise and incomplete information between frames. To address these challenges, we present MedGS, a semi-supervised neural implicit surface reconstruction framework that employs a Gaussian Splatting (GS)-based interpolation mechanism. In this framework, medical imaging data are represented as consecutive two-dimensional (2D) frames embedded in 3D space and modeled using Gaussian-based distributions. This representation enables robust frame interpolation and high-fidelity surface reconstruction across imaging modalities. As a result, MedGS offers more efficient training than traditional neural implicit methods. Its explicit GS-based representation enhances noise robustness, allows flexible editing, and supports precise modeling of complex anatomical structures with fewer artifacts. These features make MedGS highly suitable for scalable and practical applications in medical imaging.

Kornel Howil, Joanna Waczyńska, Piotr Borycki et al.

Gaussian Splatting (GS) has recently emerged as an efficient representation for rendering 3D scenes from 2D images and has been extended to images, videos, and dynamic 4D content. However, applying style transfer to GS-based representations, especially beyond simple color changes, remains challenging. In this work, we introduce CLIPGaussian, the first unified style transfer framework that supports text- and image-guided stylization across multiple modalities: 2D images, videos, 3D objects, and 4D scenes. Our method operates directly on Gaussian primitives and integrates into existing GS pipelines as a plug-in module, without requiring large generative models or retraining from scratch. The CLIPGaussian approach enables joint optimization of color and geometry in 3D and 4D settings, and achieves temporal coherence in videos, while preserving the model size. We demonstrate superior style fidelity and consistency across all tasks, validating CLIPGaussian as a universal and efficient solution for multimodal style transfer.

Krzysztof Byrski, Jacek Tabor, Przemysław Spurek et al.

In practical applications of regression analysis, it is not uncommon to encounter a multitude of values for each attribute. In such a situation, the univariate distribution, which is typically Gaussian, is suboptimal because the mean may be situated between modes, resulting in a predicted value that differs significantly from the actual data. Consequently, to address this issue, a mixture distribution with parameters learned by a neural network, known as a Mixture Density Network (MDN), is typically employed. However, this approach has an important inherent limitation, in that it is not feasible to ascertain the precise number of components with a reasonable degree of accuracy. In this paper, we introduce CEC-MMR, a novel approach based on Cross-Entropy Clustering (CEC), which allows for the automatic detection of the number of components in a regression problem. Furthermore, given an attribute and its value, our method is capable of uniquely identifying it with the underlying component. The experimental results demonstrate that CEC-MMR yields superior outcomes compared to classical MDNs.

Tadeusz Dziarmaga, Marcin Kądziołka, Artur Kasymov et al.

Deep generative models (DGMs) have caused a paradigm shift in the field of machine learning, yielding noteworthy advancements in domains such as image synthesis, natural language processing, and other related areas. However, a comprehensive evaluation of these models that accounts for the trichotomy between fidelity, diversity, and novelty in generated samples remains a formidable challenge. A recently introduced solution that has emerged as a promising approach in this regard is the Feature Likelihood Divergence (FLD), a method that offers a theoretically motivated practical tool, yet also exhibits some computational challenges. In this paper, we propose PALATE, a novel enhancement to the evaluation of DGMs that addresses limitations of existing metrics. Our approach is based on a peculiar application of the law of total expectation to random variables representing accessible real data. When combined with the MMD baseline metric and DINOv2 feature extractor, PALATE offers a holistic evaluation framework that matches or surpasses state-of-the-art solutions while providing superior computational efficiency and scalability to large-scale datasets. Through a series of experiments, we demonstrate the effectiveness of the PALATE enhancement, contributing a computationally efficient, holistic evaluation approach that advances the field of DGMs assessment, especially in detecting sample memorization and evaluating generalization capabilities.

Marcin Mazur, Tadeusz Dziarmaga, Piotr Kościelniak et al.

Since its original formulation, Jensen's inequality has played a fundamental role across mathematics, statistics, and machine learning, with its probabilistic version highlighting the nonnegativity of the so-called Jensen's gap, i.e., the difference between the expectation of a convex function and the function at the expectation. Of particular importance is the case when the function is logarithmic, as this setting underpins many applications in variational inference, where the term variational gap is often used interchangeably. Recent research has focused on estimating the size of Jensen's gap and establishing tight lower and upper bounds under various assumptions on the underlying function and distribution, driven by practical challenges such as the intractability of log-likelihood in graphical models like variational autoencoders (VAEs). In this paper, we propose new, general bounds for Jensen's gap that accommodate a broad range of assumptions on both the function and the random variable, with special attention to exponential and logarithmic cases. We provide both analytical and empirical evidence for the performance of our method. Furthermore, we relate our bounds to the PAC-Bayes framework, providing new insights into generalization performance in probabilistic models.

Magdalena Trędowicz, Marcin Mazur, Szymon Janusz et al.

Video processing is generally divided into two main categories: processing of the entire video, which typically yields optimal classification outcomes, and real-time processing, where the objective is to make a decision as promptly as possible. Although the models dedicated to the processing of entire videos are typically well-defined and clearly presented in the literature, this is not the case for online processing, where a~plethora of hand-devised methods exist. To address this issue, we present PrAViC, a novel, unified, and theoretically-based adaptation framework for tackling the online classification problem in video data. The initial phase of our study is to establish a mathematical background for the classification of sequential data, with the potential to make a decision at an early stage. This allows us to construct a natural function that encourages the model to return a result much faster. The subsequent phase is to present a straightforward and readily implementable method for adapting offline models to the online setting using recurrent operations. Finally, PrAViC is evaluated by comparing it with existing state-of-the-art offline and online models and datasets. This enables the network to significantly reduce the time required to reach classification decisions while maintaining, or even enhancing, accuracy.

Dominik Zimny, Artur Kasymov, Adam Kania et al.

NeRF is a popular model that efficiently represents 3D objects from 2D images. However, vanilla NeRF has some important limitations. NeRF must be trained on each object separately. The training time is long since we encode the object's shape and color in neural network weights. Moreover, NeRF does not generalize well to unseen data. In this paper, we present MultiPlaneNeRF -- a model that simultaneously solves the above problems. Our model works directly on 2D images. We project 3D points on 2D images to produce non-trainable representations. The projection step is not parametrized and a very shallow decoder can efficiently process the representation. Furthermore, we can train MultiPlaneNeRF on a large data set and force our implicit decoder to generalize across many objects. Consequently, we can only replace the 2D images (without additional training) to produce a NeRF representation of the new object. In the experimental section, we demonstrate that MultiPlaneNeRF achieves results comparable to state-of-the-art models for synthesizing new views and has generalization properties. Additionally, MultiPlane decoder can be used as a component in large generative models like GANs.

Marcin Mazur, Łukasz Pustelnik, Szymon Knop et al.

We propose an effective regularization strategy (CW-TaLaR) for solving continual learning problems. It uses a penalizing term expressed by the Cramer-Wold distance between two probability distributions defined on a target layer of an underlying neural network that is shared by all tasks, and the simple architecture of the Cramer-Wold generator for modeling output data representation. Our strategy preserves target layer distribution while learning a new task but does not require remembering previous tasks' datasets. We perform experiments involving several common supervised frameworks, which prove the competitiveness of the CW-TaLaR method in comparison to a few existing state-of-the-art continual learning models.

Magdalena Proszewska, Marcin Mazur, Tomasz Trzciński et al.

Recently introduced implicit field representations offer an effective way of generating 3D object shapes. They leverage implicit decoder trained to take a 3D point coordinate concatenated with a shape encoding and to output a value which indicates whether the point is outside the shape or not. Although this approach enables efficient rendering of visually plausible objects, it has two significant limitations. First, it is based on a single neural network dedicated for all objects from a training set which results in a cumbersome training procedure and its application in real life. More importantly, the implicit decoder takes only points sampled within voxels (and not the entire voxels) which yields problems at the classification boundaries and results in empty spaces within the rendered mesh. To solve the above limitations, we introduce a new HyperCube architecture based on interval arithmetic network, that enables direct processing of 3D voxels, trained using a hypernetwork paradigm to enforce model convergence. Instead of processing individual 3D samples from within a voxel, our approach allows to input the entire voxel (3D cube) represented with its convex hull coordinates, while the target network constructed by a hypernet assigns it to an inside or outside category. As a result our HyperCube model outperforms the competing approaches both in terms of training and inference efficiency, as well as the final mesh quality.

Przemysław Spurek, Sebastian Winczowski, Maciej Zięba et al.

Recently proposed 3D object reconstruction methods represent a mesh with an atlas - a set of planar patches approximating the surface. However, their application in a real-world scenario is limited since the surfaces of reconstructed objects contain discontinuities, which degrades the quality of the final mesh. This is mainly caused by independent processing of individual patches, and in this work, we postulate to mitigate this limitation by preserving local consistency around patch vertices. To that end, we introduce a Locally Conditioned Atlas (LoCondA), a framework for representing a 3D object hierarchically in a generative model. Firstly, the model maps a point cloud of an object into a sphere. Secondly, by leveraging a spherical prior, we enforce the mapping to be locally consistent on the sphere and on the target object. This way, we can sample a mesh quad on that sphere and project it back onto the object's manifold. With LoCondA, we can produce topologically diverse objects while maintaining quads to be stitched together. We show that the proposed approach provides structurally coherent reconstructions while producing meshes of quality comparable to the competitors.

Przemysław Spurek, Artur Kasymov, Marcin Mazur et al.

Scanning real-life scenes with modern registration devices typically give incomplete point cloud representations, mostly due to the limitations of the scanning process and 3D occlusions. Therefore, completing such partial representations remains a fundamental challenge of many computer vision applications. Most of the existing approaches aim to solve this problem by learning to reconstruct individual 3D objects in a synthetic setup of an uncluttered environment, which is far from a real-life scenario. In this work, we reformulate the problem of point cloud completion into an object hallucination task. Thus, we introduce a novel autoencoder-based architecture called HyperPocket that disentangles latent representations and, as a result, enables the generation of multiple variants of the completed 3D point clouds. We split point cloud processing into two disjoint data streams and leverage a hypernetwork paradigm to fill the spaces, dubbed pockets, that are left by the missing object parts. As a result, the generated point clouds are not only smooth but also plausible and geometrically consistent with the scene. Our method offers competitive performances to the other state-of-the-art models, and it enables a~plethora of novel applications.

Szymon Knop, Marcin Mazur, Przemysław Spurek et al.

Generative models dealing with modeling a~joint data distribution are generally either autoencoder or GAN based. Both have their pros and cons, generating blurry images or being unstable in training or prone to mode collapse phenomenon, respectively. The objective of this paper is to construct a~model situated between above architectures, one that does not inherit their main weaknesses. The proposed LCW generator (Latent Cramer-Wold generator) resembles a classical GAN in transforming Gaussian noise into data space. What is of utmost importance, instead of a~discriminator, LCW generator uses kernel distance. No adversarial training is utilized, hence the name generator. It is trained in two phases. First, an autoencoder based architecture, using kernel measures, is built to model a manifold of data. We propose a Latent Trick mapping a Gaussian to latent in order to get the final model. This results in very competitive FID values.

Chad Kelterborn, Marcin Mazur, Bogdan V. Petrenko

Gradient descent algorithms have been used in countless applications since the inception of Newton's method. The explosion in the number of applications of neural networks has re-energized efforts in recent years to improve the standard gradient descent method in both efficiency and accuracy. These methods modify the effect of the gradient in updating the values of the parameters. These modifications often incorporate hyperparameters: additional variables whose values must be specified at the outset of the program. We provide, below, a novel gradient descent algorithm, called Gravilon, that uses the geometry of the hypersurface to modify the length of the step in the direction of the gradient. Using neural networks, we provide promising experimental results comparing the accuracy and efficiency of the Gravilon method against commonly used gradient descent algorithms on MNIST digit classification.

Szymon Knop, Marcin Mazur, Jacek Tabor et al.

In this paper we discuss a class of AutoEncoder based generative models based on one dimensional sliced approach. The idea is based on the reduction of the discrimination between samples to one-dimensional case. Our experiments show that methods can be divided into two groups. First consists of methods which are a modification of standard normality tests, while the second is based on classical distances between samples. It turns out that both groups are correct generative models, but the second one gives a slightly faster decrease rate of Fréchet Inception Distance (FID).

Szymon Knop, Jacek Tabor, Przemysław Spurek et al.

We propose a new generative model, Cramer-Wold Autoencoder (CWAE). Following WAE, we directly encourage normality of the latent space. Our paper uses also the recent idea from Sliced WAE (SWAE) model, which uses one-dimensional projections as a method of verifying closeness of two distributions. The crucial new ingredient is the introduction of a new (Cramer-Wold) metric in the space of densities, which replaces the Wasserstein metric used in SWAE. We show that the Cramer-Wold metric between Gaussian mixtures is given by a simple analytic formula, which results in the removal of sampling necessary to estimate the cost function in WAE and SWAE models. As a consequence, while drastically simplifying the optimization procedure, CWAE produces samples of a matching perceptual quality to other SOTA models.