arXiv subjects

Gabriel Raya

Publications and source records attributed to Gabriel Raya.

7 recordsLinked to original sources

arXiv2026

From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime

How should a diffusion model decide which noise levels to train on, and how much? Despite the importance of this choice, current noise schedules are based largely on heuristics or empirical tuning. Here, we develop a general statistical framework for studying asymptotically optimal noise-level allocation in diffusion training. Our first main result concerns the fully coupled regime, where information can spread between different time points. Under convexity or Polyak-Lojasiewicz-type assumptions, we show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels. Our second main result specializes this framework to an idealized independent-learner regime, intended to model temporal specialization in neural networks. Under an additional feature-noise decoupling condition, a random-matrix analysis leads to an information-theoretic proxy: the decoupled sampling density is proportional to the square root of the generative entropy rate, the rate at which conditional entropy grows along the forward process. We test these predictions in controlled settings where the coupled objective can be optimized directly, including Dirac mixtures, low-dimensional manifolds, and MNIST. In these settings, the optimized schedules are consistently finite-support, while the smooth entropic proxy closely tracks the atomic optimum in neural-network models and breaks down mainly in the fully coupled parametric case, as the theory suggests. We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable. The results indicate that square-root entropy scheduling can substantially improve training efficiency on discrete domains and remains competitive with standard EDM-style heuristics on continuous images.

cs.LG↗

arXiv2026

Noise Scheduling as Information-Guided Allocation in Diffusion Training

We introduce InfoNoise, an online adaptive noise schedule for diffusion training that reallocates optimization effort toward noise levels where denoising is most informative. Together with loss weighting, a noise schedule induces an effective allocation across denoising problems, often fixed before informative noise levels are known. InfoNoise makes this allocation data-adaptive by estimating a conditional-entropy-rate profile from denoising losses during training, without auxiliary models or offline search. Through I--MMSE, this profile identifies where noisy observations rapidly reduce uncertainty about the clean sample and guides adaptation of the training noise distribution. It changes only this distribution, keeping the objective, weighting, and parameterization fixed. On image benchmarks, where schedules have been extensively tuned, InfoNoise matches or slightly exceeds strong baselines and can reach the same quality with fewer updates. On representation, sequence, and modality shifts, including DNA and language generation, InfoNoise improves over fixed and adaptive baselines and reaches target quality with up to $3\times$ less training compute. These results establish the conditional-entropy-rate profile as the data-dependent target for noise schedule design and make online adaptation a practical alternative to manual schedule search.

cs.LG↗

arXiv2025

Measuring Semantic Information Production in Generative Diffusion Models

It is well known that semantic and structural features of the generated images emerge at different times during the reverse dynamics of diffusion, a phenomenon that has been connected to physical phase transitions in magnets and other materials. In this paper, we introduce a general information-theoretic approach to measure when these class-semantic "decisions" are made during the generative process. By using an online formula for the optimal Bayesian classifier, we estimate the conditional entropy of the class label given the noisy state. We then determine the time intervals corresponding to the highest information transfer between noisy states and class labels using the time derivative of the conditional entropy. We demonstrate our method on one-dimensional Gaussian mixture models and on DDPM models trained on the CIFAR10 dataset. As expected, we find that the semantic information transfer is highest in the intermediate stages of diffusion while vanishing during the final stages. However, we found sizable differences between the entropy rate profiles of different classes, suggesting that different "semantic decisions" are located at different intermediate times.

stat.ML↗

arXiv2025

Memorization to Generalization: Emergence of Diffusion Models from Associative Memory

Dense Associative Memories (DenseAMs) are generalizations of Hopfield networks, which have superior information storage capacity and can store training data points (memories) at local minima of the energy landscape. When the amount of training data exceeds the critical memory storage capacity of these models, new local minima, which are different from the training data, emerge. In Associative Memory these emergent local minima are called $\textit{spurious}\; \textit{states}$, which hinder memory retrieval. In this work, we examine diffusion models (DMs) through the DenseAM lens, viewing their generative process as an attempt of a memory retrieval. In the small data regimes, DMs create distinct attractors for each training sample, akin to DenseAMs below the critical memory storage. As the training data size increases, they transition from memorization to generalization. We identify a critical intermediate phase, predicted by DenseAM theory -- the spurious states. In generative modeling, these states are no longer negative artifacts but rather are the first signs of generative capabilities. We characterize the basins of attraction, energy landscape curvature, and computational properties of these previously overlooked states. Their existence is demonstrated across a wide range of architectures and datasets.

cs.LG↗

arXiv2024

Dynamic Negative Guidance of Diffusion Models

Negative Prompting (NP) is widely utilized in diffusion models, particularly in text-to-image applications, to prevent the generation of undesired features. In this paper, we show that conventional NP is limited by the assumption of a constant guidance scale, which may lead to highly suboptimal results, or even complete failure, due to the non-stationarity and state-dependence of the reverse process. Based on this analysis, we derive a principled technique called Dynamic Negative Guidance, which relies on a near-optimal time and state dependent modulation of the guidance without requiring additional training. Unlike NP, negative guidance requires estimating the posterior class probability during the denoising process, which is achieved with limited additional computational overhead by tracking the discrete Markov Chain during the generative process. We evaluate the performance of DNG class-removal on MNIST and CIFAR10, where we show that DNG leads to higher safety, preservation of class balance and image quality when compared with baseline methods. Furthermore, we show that it is possible to use DNG with Stable Diffusion to obtain more accurate and less invasive guidance than NP.

cs.CV↗

arXiv2024

Losing dimensions: Geometric memorization in generative diffusion

Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion models experience a smooth collapse where their capacity to vary across independent directions diminishes. Measuring latent dimensionality via the learned score field, we reveal how generative behavior increasingly centers on a few examples while other variations "freeze out". We propose a geometric memorization theory, showing that salient features collapse first, then finer details, leading to near point-wise replication. This mirrors physical systems condensing into a few low-energy configurations. Our theoretical predictions align with both synthetic and real data, identifying geometric memorization as a distinct phase between generalization and exact copying.

stat.ML↗

arXiv2023

Spontaneous Symmetry Breaking in Generative Diffusion Models

Generative diffusion models have recently emerged as a leading approach for generating high-dimensional data. In this paper, we show that the dynamics of these models exhibit a spontaneous symmetry breaking that divides the generative dynamics into two distinct phases: 1) A linear steady-state dynamics around a central fixed-point and 2) an attractor dynamics directed towards the data manifold. These two "phases" are separated by the change in stability of the central fixed-point, with the resulting window of instability being responsible for the diversity of the generated samples. Using both theoretical and empirical evidence, we show that an accurate simulation of the early dynamics does not significantly contribute to the final generation, since early fluctuations are reverted to the central fixed point. To leverage this insight, we propose a Gaussian late initialization scheme, which significantly improves model performance, achieving up to 3x FID improvements on fast samplers, while also increasing sample diversity (e.g., racial composition of generated CelebA images). Our work offers a new way to understand the generative dynamics of diffusion models that has the potential to bring about higher performance and less biased fast-samplers.

cs.LG↗