Imaging systems have traditionally been designed to mimic the human eye and produce visually interpretable measurements.

Diffusion models (DMs) excel in image generation but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers for DMs accelerate denoising inference, they often lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers a reference-free way to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called EVODiff, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to 45.5% (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by 25% (from 20 to 15 NFE) for highquality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts.

The practical performance of generative diffusion models depends on the appropriate choice of the noise scheduling function, which can also be equivalently expressed as a time reparameterization. In this paper, we present a time scheduler that selects sampling points based on entropy rather than uniform time spacing, ensuring that each point contributes an equal amount of information to the final generation. We prove that this time reparameterization does not depend on the initial choice of time. Furthermore, we provide a tractable exact formula to estimate this entropic time for a trained model using the training loss without substantial overhead. Alongside the entropic time, inspired by the optimality results, we introduce a rescaled entropic time. In our experiments with mixtures of Gaussian distributions and ImageNet, we show that using the (rescaled) entropic times greatly improves the inference performance of trained models. In particular, we found that the image quality in pretrained EDM2 models, as evaluated by FID and FD-DINO scores, can be substantially increased by the rescaled entropic time reparameterization without increasing the number of function evaluations, with greater improvements in the few NFEs regime. Code is available at https://github.com/DejanStancevic/

Diffusion models (DMs) excel in image generation but suffer from slow inference and training-inference discrepancies. Although gradient-based solvers for DMs accelerate denoising inference, they often lack theoretical foundations in information transmission efficiency. In this work, we introduce an information-theoretic perspective on the inference processes of DMs, revealing that successful denoising fundamentally reduces conditional entropy in reverse transitions. This principle leads to our key insights into the inference processes: (1) data prediction parameterization outperforms its noise counterpart, and (2) optimizing conditional variance offers to minimize both transition and reconstruction errors. Based on these insights, we propose an entropy-aware variance optimized method for the generative process of DMs, called, which systematically reduces uncertainty by optimizing conditional entropy during denoising. Extensive experiments on DMs validate our insights and demonstrate that our method significantly and consistently outperforms state-of-the-art (SOTA) gradient-based solvers. For example, compared to the DPM-Solver++, EVODiff reduces the reconstruction error by up to (FID improves from 5.10 to 2.78) at 10 function evaluations (NFE) on CIFAR-10, cuts the NFE cost by (from 20 to 15 NFE) for high-quality samples on ImageNet-256, and improves text-to-image generation while reducing artifacts.

A significant use case of instruction-finetuned Large Language Models (LLMs) is to solve question-answering tasks interactively. In this setting, an LLM agent is tasked with making a prediction by sequentially querying relevant information from the user, as opposed to a single-turn conversation. This paper explores sequential querying strategies that aim to minimize the expected number of queries. One such strategy is Information Pursuit (IP), a greedy algorithm that at each iteration selects the query that maximizes information gain or equivalently minimizes uncertainty. However, obtaining accurate estimates of mutual information or conditional entropy for LLMs is very difficult in practice due to over-or under-confident LLM probabilities, which leads to suboptimal query selection and predictive performance.

Neural Information Processing Systems http://nips.cc/

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

The practical performance of generative diffusion models depends on the appropriate choice of the noise scheduling function, which can also be equivalently expressed as a time reparameterization. In this paper, we present a time scheduler that selects sampling points based on entropy rather than uniform time spacing, ensuring that each point contributes an equal amount of information to the final generation. We prove that this time reparameterization does not depend on the initial choice of time. Furthermore, we provide a tractable exact formula to estimate this \emph{entropic time} for a trained model using the training loss without substantial overhead. Alongside the entropic time, inspired by the optimality results, we introduce a rescaled entropic time. In our experiments with mixtures of Gaussian distributions and ImageNet, we show that using the (rescaled) entropic times greatly improves the inference performance of trained models. In particular, we found that the image quality in pretrained EDM2 models, as evaluated by FID and FD-DINO scores, can be substantially increased by the rescaled entropic time reparameterization without increasing the number of function evaluations, with greater improvements in the few NFEs regime. Code is available at https://github.com/DejanStancevic/Entropic-Time-Schedulers-for-Generative-Diffusion-Models.