Conditional diffusion models have shown remarkable success in visual content generation, producing high-quality samples across various domains, largely due to classifier-free guidance (CFG). Recent attempts to extend guidance to unconditional models have relied on heuristic techniques, resulting in suboptimal generation quality and unintended effects. In this work, we propose Smoothed Energy Guidance (SEG), a novel training-and condition-free approach that leverages the energy-based perspective of the self-attention mechanism to enhance image generation. By defining the energy of self-attention, we introduce a method to reduce the curvature of the energy landscape of attention and use the output as the unconditional prediction. Practically, we control the curvature of the energy landscape by adjusting the Gaussian kernel parameter while keeping the guidance scale parameter fixed. Additionally, we present a query blurring method that is equivalent to blurring the entire attention weights without incurring quadratic complexity in the number of tokens. In our experiments, SEG achieves a Pareto improvement in both quality and the reduction of side effects.

The storage of continuous variables in working memory is hypothesized to be sustained in the brain by the dynamics of recurrent neural networks (RNNs) whose steady states form continuous manifolds. In some cases, it is thought that the synaptic connectivity supports multiple attractor manifolds, each mapped to a different context or task. For example, in hippocampal area CA3, positions in distinct environments are represented by distinct sets of population activity patterns, each forming a continuum. It has been argued that the embedding of multiple continuous attractors in a single RNN inevitably causes detrimental interference: quenched noise in the synaptic connectivity disrupts the continuity of each attractor, replacing it by a discrete set of steady states that can be conceptualized as lying on local minima of an abstract energy landscape. Consequently, population activity patterns exhibit systematic drifts towards one of these discrete minima, thereby degrading the stored memory over time. Here we show that it is possible to dramatically attenuate these detrimental interference effects by adjusting the synaptic weights. Synaptic weight adjustment are derived from a loss function that quantifies the roughness of the energy landscape along each of the embedded attractor manifolds. By minimizing this loss function, the stability of states can be dramatically improved, without compromising the capacity.

Urban transportation systems face increasing resilience challenges from extreme weather events, but current assessment methods rely on surface-level recovery indicators that miss hidden structural damage. Existing approaches cannot distinguish between true recovery and "false recovery," where traffic metrics normalize, but the underlying system dynamics permanently degrade. To address this, a new physics-constrained Hamiltonian learning algorithm combining "structural irreversibility detection" and "energy landscape reconstruction" has been developed. Our approach extracts low-dimensional state representations, identifies quasi-Hamiltonian structures through physics-constrained optimization, and quantifies structural changes via energy landscape comparison. Analysis of London's extreme rainfall in 2021 demonstrates that while surface indicators were fully recovered, our algorithm detected 64.8\% structural damage missed by traditional monitoring. Our framework provides tools for proactive structural risk assessment, enabling infrastructure investments based on true system health rather than misleading surface metrics.

Guidance techniques are commonly used in diffusion and flow models to improve image quality and input consistency for conditional generative tasks such as class-conditional and text-to-image generation. In particular, classifier-free guidance (CFG) is the most widely adopted guidance technique. It results, however, in trade-offs across quality, diversity and consistency: improving some at the expense of others. While recent work has shown that it is possible to disentangle these factors to some extent, such methods come with an overhead of requiring an additional (weaker) model, or require more forward passes per sampling step. In this paper, we propose Entropy Rectifying Guidance (ERG), a simple and effective guidance method based on inference-time changes in the attention mechanism of state-of-the-art diffusion transformer architectures, which allows for simultaneous improvements over image quality, diversity and prompt consistency. ERG is more general than CFG and similar guidance techniques, as it extends to unconditional sampling. We show that ERG results in significant improvements in various tasks, including text-to-image, class-conditional and unconditional image generation. We also show that ERG can be seamlessly combined with other recent guidance methods such as CADS and APG, further improving generation results.

Recent attempts to extend guidance to unconditional models have relied on heuristic techniques, resulting in suboptimal generation quality and unintended effects.

Structured prediction energy networks (SPENs) (Belanger & McCallum, 2016) are a type of energy-based model (LeCun et al., 2006) in which inference is done by gradient descent.

The dynamics of neural activity are described by a standard rate model. Note that only the third term of Eq. 'th place cell preferred firing position in the's are standard unit vectors spanning an orthonormal basis. To derive Eq. 3 we evaluate the derivative of Energy landscapes were uniformly shifted throughout the manuscript by a constant (Figs. For each network with a different number of total embedded maps, 15 realizations were performed in which the permutations between the spatial maps were chosen independently and at random. Code availability Code is available at public repository https://doi.org/10.5281/zenodo.10016179.

We address the challenge of training diffusion models to sample from unnormalized energy distributions in the absence of data, the so-called diffusion samplers. Although these approaches have shown promise, they struggle to scale in more demanding scenarios where energy evaluations are expensive and the sampling space is high-dimensional. To address this limitation, we propose a scalable and sample-efficient framework that properly harmonizes the powerful classical sampling method and the diffusion sampler. Specifically, we utilize Monte Carlo Markov chain (MCMC) samplers with a novelty-based auxiliary energy as a Searcher to collect off-policy samples, using an auxiliary energy function to compensate for exploring modes the diffusion sampler rarely visits. These off-policy samples are then combined with on-policy data to train the diffusion sampler, thereby expanding its coverage of the energy landscape. Furthermore, we identify primacy bias, i.e., the preference of samplers for early experience during training, as the main cause of mode collapse during training, and introduce a periodic re-initialization trick to resolve this issue. Our method significantly improves sample efficiency on standard benchmarks for diffusion samplers and also excels at higher-dimensional problems and real-world molecular conformer generation.

What is the shortest path between two data points lying in a high-dimensional space? While the answer is trivial in Euclidean geometry, it becomes significantly more complex when the data lies on a curved manifold -- requiring a Riemannian metric to describe the space's local curvature. Estimating such a metric, however, remains a major challenge in high dimensions. In this work, we propose a method for deriving Riemannian metrics directly from pretrained Energy-Based Models (EBMs) -- a class of generative models that assign low energy to high-density regions. These metrics define spatially varying distances, enabling the computation of geodesics -- shortest paths that follow the data manifold's intrinsic geometry. We introduce two novel metrics derived from EBMs and show that they produce geodesics that remain closer to the data manifold and exhibit lower curvature distortion, as measured by alignment with ground-truth trajectories. We evaluate our approach on increasingly complex datasets: synthetic datasets with known data density, rotated character images with interpretable geometry, and high-resolution natural images embedded in a pretrained VAE latent space. Our results show that EBM-derived metrics consistently outperform established baselines, especially in high-dimensional settings. Our work is the first to derive Riemannian metrics from EBMs, enabling data-aware geodesics and unlocking scalable, geometry-driven learning for generative modeling and simulation.