Improved Sampling Schedules for Discrete Diffusion Models

Discrete diffusion models have emerged as a powerful paradigm for generative modeling on sequence data; however, the information-theoretic principles governing their reverse processes remain significantly less understood than those of their continuous counterparts. In this work, we bridge this gap by analyzing the reverse process dynamics through the lens of thermodynamic entropy production. We propose the entropy production rate as a rigorous proxy for quantifying information generation, deriving as a byproduct a bound on the Wasserstein distance between intermediate states and the data distribution. Leveraging these insights, we introduce two novel sampling schedules that are uniformly spaced with respect to their corresponding physics-inspired metrics: the Entropic Discrete Schedule (EDS), which is defined by maintaining a constant rate of information gain, and the Wasserstein Discrete Schedule (WDS), which is defined by taking equal steps in terms of the Wasserstein distance. We empirically demonstrate that our proposed schedules significantly outperform state-of-the-art strategies across diverse application domains, including synthetic data, music notation, vision and language modeling, consistently achieving superior performance at a lower computational budget.

TENDE: Transfer Entropy Neural Diffusion Estimation

Transfer entropy measures directed information flow in time series, and it has become a fundamental quantity in applications spanning neuroscience, finance, and complex systems analysis. However, existing estimation methods suffer from the curse of dimensionality, require restrictive distributional assumptions, or need exponentially large datasets for reliable convergence. We address these limitations in the literature by proposing TENDE (Transfer Entropy Neural Diffusion Estimation), a novel approach that leverages score-based diffusion models to estimate transfer entropy through conditional mutual information. By learning score functions of the relevant conditional distributions, TENDE provides flexible, scalable estimation while making minimal assumptions about the underlying data-generating process. We demonstrate superior accuracy and robustness compared to existing neural estimators and other state-of-the-art approaches across synthetic benchmarks and real data.

Scaling Laws for Uncertainty in Deep Learning

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the over-parameterized regime, we examine a parallel direction: do similar scaling laws govern predictive uncertainties in deep learning? In identifiable parametric models, such scaling laws can be derived in a straightforward manner by treating model parameters in a Bayesian way. In this case, for example, we obtain $O(1/N)$ contraction rates for epistemic uncertainty with respect to the number of data $N$. However, in over-parameterized models, these guarantees do not hold, leading to largely unexplored behaviors. In this work, we empirically show the existence of scaling laws associated with various measures of predictive uncertainty with respect to dataset and model sizes. Through experiments on vision and language tasks, we observe such scaling laws for in- and out-of-distribution predictive uncertainty estimated through popular approximate Bayesian inference and ensemble methods. Besides the elegance of scaling laws and the practical utility of extrapolating uncertainties to larger data or models, this work provides strong evidence to dispel recurring skepticism against Bayesian approaches: "In many applications of deep learning we have so much data available: what do we need Bayes for?". Our findings show that "so much data" is typically not enough to make epistemic uncertainty negligible.

RFMI: Estimating Mutual Information on Rectified Flow for Text-to-Image Alignment

Rectified Flow (RF) models trained with a Flow matching framework have achieved state-of-the-art performance on Text-to-Image (T2I) conditional generation. Yet, multiple benchmarks show that synthetic images can still suffer from poor alignment with the prompt, i.e., images show wrong attribute binding, subject positioning, numeracy, etc. While the literature offers many methods to improve T2I alignment, they all consider only Diffusion Models, and require auxiliary datasets, scoring models, and linguistic analysis of the prompt. In this paper we aim to address these gaps. First, we introduce RFMI, a novel Mutual Information (MI) estimator for RF models that uses the pre-trained model itself for the MI estimation. Then, we investigate a self-supervised fine-tuning approach for T2I alignment based on RFMI that does not require auxiliary information other than the pre-trained model itself. Specifically, a fine-tuning set is constructed by selecting synthetic images generated from the pre-trained RF model and having high point-wise MI between images and prompts. Our experiments on MI estimation benchmarks demonstrate the validity of RFMI, and empirical fine-tuning on SD3.5-Medium confirms the effectiveness of RFMI for improving T2I alignment while maintaining image quality.

Learning to Match Unpaired Data with Minimum Entropy Coupling

Multimodal data is a precious asset enabling a variety of downstream tasks in machine learning. However, real-world data collected across different modalities is often not paired, which is a significant challenge to learn a joint distribution. A prominent approach to address the modality coupling problem is Minimum Entropy Coupling (MEC), which seeks to minimize the joint Entropy, while satisfying constraints on the marginals. Existing approaches to the MEC problem focus on finite, discrete distributions, limiting their application for cases involving continuous data. In this work, we propose a novel method to solve the continuous MEC problem, using well-known generative diffusion models that learn to approximate and minimize the joint Entropy through a cooperative scheme, while satisfying a relaxed version of the marginal constraints. We empirically demonstrate that our method, DDMEC, is general and can be easily used to address challenging tasks, including unsupervised single-cell multi-omics data alignment and unpaired image translation, outperforming specialized methods.

INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators

Information-theoretic quantities play a crucial role in understanding non-linear relationships between random variables and are widely used across scientific disciplines. However, estimating these quantities remains an open problem, particularly in the case of high-dimensional discrete distributions. Current approaches typically rely on embedding discrete data into a continuous space and applying neural estimators originally designed for continuous distributions, a process that may not fully capture the discrete nature of the underlying data. We consider Continuous-Time Markov Chains (CTMCs), stochastic processes on discrete state-spaces which have gained popularity due to their generative modeling applications. In this work, we introduce INFO-SEDD, a novel method for estimating information-theoretic quantities of discrete data, including mutual information and entropy. Our approach requires the training of a single parametric model, offering significant computational and memory advantages. Additionally, it seamlessly integrates with pretrained networks, allowing for efficient reuse of pretrained generative models. To evaluate our approach, we construct a challenging synthetic benchmark. Our experiments demonstrate that INFO-SEDD is robust and outperforms neural competitors that rely on embedding techniques. Moreover, we validate our method on a real-world task: estimating the entropy of an Ising model. Overall, INFO-SEDD outperforms competing methods and shows scalability to high-dimensional scenarios, paving the way for new applications where estimating MI between discrete distribution is the focus. The promising results in this complex, high-dimensional scenario highlight INFO-SEDD as a powerful new estimator in the toolkit for information-theoretical analysis.

In Praise of Stubbornness: The Case for Cognitive-Dissonance-Aware Knowledge Updates in LLMs

Despite remarkable capabilities, large language models (LLMs) struggle to continually update their knowledge without catastrophic forgetting. In contrast, humans effortlessly integrate new information, detect conflicts with existing beliefs, and selectively update their mental models. This paper introduces a cognitive-inspired investigation paradigm to study continual knowledge updating in LLMs. We implement two key components inspired by human cognition: (1) Dissonance and Familiarity Awareness, analyzing model behavior to classify information as novel, familiar, or dissonant; and (2) Targeted Network Updates, which track neural activity to identify frequently used (stubborn) and rarely used (plastic) neurons. Through carefully designed experiments in controlled settings, we uncover a number of empirical findings demonstrating the potential of this approach. First, dissonance detection is feasible using simple activation and gradient features, suggesting potential for cognitive-inspired training. Second, we find that non-dissonant updates largely preserve prior knowledge regardless of targeting strategy, revealing inherent robustness in LLM knowledge integration. Most critically, we discover that dissonant updates prove catastrophically destructive to the model's knowledge base, indiscriminately affecting even information unrelated to the current updates. This suggests fundamental limitations in how neural networks handle contradictions and motivates the need for new approaches to knowledge updating that better mirror human cognitive mechanisms.

Latent Abstractions in Generative Diffusion Models

In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We present a novel theoretical framework that extends NLF, and that offers a unique perspective on SDE-based generative models. The development of our theory relies on a novel formulation of the joint (state and measurement) dynamics, and an information-theoretic measure of the influence of the system state on the measurement process. According to our theory, diffusion models can be cast as a system of SDE, describing a non-linear filter in which the evolution of unobservable latent abstractions steers the dynamics of an observable measurement process (corresponding to the generative pathways). In addition, we present an empirical study to validate our theory and previous empirical results on the emergence of latent abstractions at different stages of the generative process.

Information Theoretic Text-to-Image Alignment

Diffusion models for Text-to-Image (T2I) conditional generation have seen tremendous success recently. Despite their success, accurately capturing user intentions with these models still requires a laborious trial and error process. This challenge is commonly identified as a model alignment problem, an issue that has attracted considerable attention by the research community. Instead of relying on fine-grained linguistic analyses of prompts, human annotation, or auxiliary vision-language models to steer image generation, in this work we present a novel method that relies on an information-theoretic alignment measure. In a nutshell, our method uses self-supervised fine-tuning and relies on point-wise mutual information between prompts and images to define a synthetic training set to induce model alignment. Our comparative analysis shows that our method is on-par or superior to the state-of-the-art, yet requires nothing but a pre-trained denoising network to estimate MI and a lightweight fine-tuning strategy.

S$Ω$I: Score-based O-INFORMATION Estimation

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce S$\Omega$I, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of S$\Omega$I in the context of a real-world use case.