Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesis

• URL: http://arxiv.org/abs/2506.21731v2
• Date: Mon, 22 Sep 2025 22:05:16 GMT
• Title: Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesis
• Authors: Chenqiu Zhao, Anup Basu,
• Abstract summary: A common assumption in probabilistic generative models for image generation is that learning the global data distribution suffices to generate novel images via sampling.<n>We investigate the limitation of this core assumption, namely that learning global distributions leads to memorization rather than generative behavior.
• Score: 9.946694131713611
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A common assumption in probabilistic generative models for image generation is that learning the global data distribution suffices to generate novel images via sampling. We investigate the limitation of this core assumption, namely that learning global distributions leads to memorization rather than generative behavior. We propose two theoretical frameworks, the Mutually Exclusive Probability Space (MEPS) and the Local Dependence Hypothesis (LDH), for investigation. MEPS arises from the observation that deterministic mappings (e.g. neural networks) involving random variables tend to reduce overlap coefficients among involved random variables, thereby inducing exclusivity. We further propose a lower bound in terms of the overlap coefficient, and introduce a Binary Latent Autoencoder (BL-AE) that encodes images into signed binary latent representations. LDH formalizes dependence within a finite observation radius, which motivates our $\gamma$-Autoregressive Random Variable Model ($\gamma$-ARVM). $\gamma$-ARVM is an autoregressive model, with a variable observation range $\gamma$, that predicts a histogram for the next token. Using $\gamma$-ARVM, we observe that as the observation range increases, autoregressive models progressively shift toward memorization. In the limit of global dependence, the model behaves as a pure memorizer when operating on the binary latents produced by our BL-AE. Comprehensive experiments and discussions support our investigation.

Related papers

• Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation [2.9810923705287524]
  In medical image analysis, deep learning models have demonstrated remarkable performance.<n>Deep generative models such as variational autoencoders (VAEs) exhibit significant generative power.<n>Probability models like sum-product networks (SPNs) efficiently represent complex joint probability distributions.
  arXiv  Detail & Related papers  (2025-07-25T15:19:32Z)
• Spatial Reasoning with Denoising Models [49.83744014336816]
  We introduce a framework to perform reasoning over sets of continuous variables via denoising generative models.<n>For the first time, that order of generation can successfully be predicted by the denoising network itself.<n>Using these findings, we can increase the accuracy of specific reasoning tasks from 1% to >50%.
  arXiv  Detail & Related papers  (2025-02-28T14:08:30Z)
• Learning Mixtures of Experts with EM: A Mirror Descent Perspective [28.48469221248906]
  Classical Mixtures of Experts (MoE) are Machine Learning models that involve the input space, with a separate "expert" model trained on each partition.<n>We study theoretical guarantees of the Expectation Maximization (EM) algorithm for the training of MoE models.
  arXiv  Detail & Related papers  (2024-11-09T03:44:09Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Time-series Generation by Contrastive Imitation [87.51882102248395]
  We study a generative framework that seeks to combine the strengths of both: Motivated by a moment-matching objective to mitigate compounding error, we optimize a local (but forward-looking) transition policy. At inference, the learned policy serves as the generator for iterative sampling, and the learned energy serves as a trajectory-level measure for evaluating sample quality.
  arXiv  Detail & Related papers  (2023-11-02T16:45:25Z)
• General Identifiability and Achievability for Causal Representation Learning [33.80247458590611]
  The paper establishes identifiability and achievability results using two hard uncoupled interventions per node in the latent causal graph. For identifiability, the paper establishes that perfect recovery of the latent causal model and variables is guaranteed under uncoupled interventions. The analysis, additionally, recovers the identifiability result for two hard coupled interventions, that is when metadata about the pair of environments that have the same node intervened is known.
  arXiv  Detail & Related papers  (2023-10-24T01:47:44Z)
• Delta-AI: Local objectives for amortized inference in sparse graphical models [64.5938437823851]
  We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs) Our approach is based on the observation that when the sampling of variables in a PGM is seen as a sequence of actions taken by an agent, sparsity of the PGM enables local credit assignment in the agent's policy learning objective. We illustrate $Delta$-AI's effectiveness for sampling from synthetic PGMs and training latent variable models with sparse factor structure.
  arXiv  Detail & Related papers  (2023-10-03T20:37:03Z)
• Prototype-based Aleatoric Uncertainty Quantification for Cross-modal Retrieval [139.21955930418815]
  Cross-modal Retrieval methods build similarity relations between vision and language modalities by jointly learning a common representation space. However, the predictions are often unreliable due to the Aleatoric uncertainty, which is induced by low-quality data, e.g., corrupt images, fast-paced videos, and non-detailed texts. We propose a novel Prototype-based Aleatoric Uncertainty Quantification (PAU) framework to provide trustworthy predictions by quantifying the uncertainty arisen from the inherent data ambiguity.
  arXiv  Detail & Related papers  (2023-09-29T09:41:19Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Improving Neural Additive Models with Bayesian Principles [54.29602161803093]
  Neural additive models (NAMs) enhance the transparency of deep neural networks by handling calibrated input features in separate additive sub-networks. We develop Laplace-approximated NAMs (LA-NAMs) which show improved empirical performance on datasets and challenging real-world medical tasks.
  arXiv  Detail & Related papers  (2023-05-26T13:19:15Z)
• Unsupervised representation learning with recognition-parametrised probabilistic models [12.865596223775649]
  We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model ( RPM) Under the key assumption that observations are conditionally independent given latents, the RPM combines parametric prior observation-conditioned latent distributions with non-parametric observationfactors. The RPM provides a powerful framework to discover meaningful latent structure underlying observational data, a function critical to both animal and artificial intelligence.
  arXiv  Detail & Related papers  (2022-09-13T00:33:21Z)
• Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis [7.895866278697778]
  Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, this assumption is almost always violated due to distribution shifts between environments. We propose the Mechanism Shift Score (MSS), a score-based approach amenable to various empirical estimators.
  arXiv  Detail & Related papers  (2022-06-04T15:39:30Z)
• Inverting brain grey matter models with likelihood-free inference: a tool for trustable cytoarchitecture measurements [62.997667081978825]
  characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI. We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells. We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
  arXiv  Detail & Related papers  (2021-11-15T09:08:27Z)
• Regularizing Variational Autoencoder with Diversity and Uncertainty Awareness [61.827054365139645]
  Variational Autoencoder (VAE) approximates the posterior of latent variables based on amortized variational inference. We propose an alternative model, DU-VAE, for learning a more Diverse and less Uncertain latent space.
  arXiv  Detail & Related papers  (2021-10-24T07:58:13Z)
• Continual Learning with Fully Probabilistic Models [70.3497683558609]
  We present an approach for continual learning based on fully probabilistic (or generative) models of machine learning. We propose a pseudo-rehearsal approach using a Gaussian Mixture Model (GMM) instance for both generator and classifier functionalities. We show that GMR achieves state-of-the-art performance on common class-incremental learning problems at very competitive time and memory complexity.
  arXiv  Detail & Related papers  (2021-04-19T12:26:26Z)
• Binary Classification of Gaussian Mixtures: Abundance of Support Vectors, Benign Overfitting and Regularization [39.35822033674126]
  We study binary linear classification under a generative Gaussian mixture model. We derive novel non-asymptotic bounds on the classification error of the latter. Our results extend to a noisy model with constant probability noise flips.
  arXiv  Detail & Related papers  (2020-11-18T07:59:55Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• CQ-VAE: Coordinate Quantized VAE for Uncertainty Estimation with Application to Disk Shape Analysis from Lumbar Spine MRI Images [1.5841288368322592]
  We propose a powerful generative model to learn a representation of ambiguity and to generate probabilistic outputs. Our model, named Coordinate Quantization Variational Autoencoder (CQ-VAE), employs a discrete latent space with an internal discrete probability distribution. A matching algorithm is used to establish the correspondence between model-generated samples and "ground-truth" samples.
  arXiv  Detail & Related papers  (2020-10-17T04:25:32Z)
• Generative Model without Prior Distribution Matching [26.91643368299913]
  Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution. We propose to let the prior match the embedding distribution rather than imposing the latent variables to fit the prior.
  arXiv  Detail & Related papers  (2020-09-23T09:33:24Z)
• Uncertainty Inspired RGB-D Saliency Detection [70.50583438784571]
  We propose the first framework to employ uncertainty for RGB-D saliency detection by learning from the data labeling process. Inspired by the saliency data labeling process, we propose a generative architecture to achieve probabilistic RGB-D saliency detection. Results on six challenging RGB-D benchmark datasets show our approach's superior performance in learning the distribution of saliency maps.
  arXiv  Detail & Related papers  (2020-09-07T13:01:45Z)
• Manifold GPLVMs for discovering non-Euclidean latent structure in neural data [5.949779668853555]
  A common problem in neuroscience is to elucidate the collective neural representations of behaviorally important variables. Here, we propose a new probabilistic latent variable model to simultaneously identify the latent state and the way each neuron contributes to its representation.
  arXiv  Detail & Related papers  (2020-06-12T19:08:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.