This paper presents a practical application of Relative Trajectory Balance (RTB), a recently introduced off-policy reinforcement learning (RL) objective that can asymptotically solve Bayesian inverse problems optimally. We extend the original work by using RTB to train conditional diffusion model posteriors from pretrained unconditional priors for challenging linear and non-linear inverse problems in vision, and science. We use the objective alongside techniques such as off-policy backtracking exploration to improve training. Importantly, our results show that existing training-free diffusion posterior methods struggle to perform effective posterior inference in latent space due to inherent biases.

Diffusion Probabilistic Models (DPMs) are powerful generative models that have achieved unparalleled success in a number of generative tasks. In this work, we aim to build inductive biases into the training and sampling of diffusion models to better accommodate the target distribution of the data to model. For topologically structured data, we devise a frequency-based noising operator to purposefully manipulate, and set, these inductive biases. We first show that appropriate manipulations of the noising forward process can lead DPMs to focus on particular aspects of the distribution to learn. We show that different datasets necessitate different inductive biases, and that appropriate frequency-based noise control induces increased generative performance compared to standard diffusion. Finally, we demonstrate the possibility of ignoring information at particular frequencies while learning. We show this in an image corruption and recovery task, where we train a DPM to recover the original target distribution after severe noise corruption.

Any well-behaved generative model over a variable $\mathbf{x}$ can be expressed as a deterministic transformation of an exogenous ('outsourced') Gaussian noise variable $\mathbf{z}$: $\mathbf{x}=f_\theta(\mathbf{z})$. In such a model (e.g., a VAE, GAN, or continuous-time flow-based model), sampling of the target variable $\mathbf{x} \sim p_\theta(\mathbf{x})$ is straightforward, but sampling from a posterior distribution of the form $p(\mathbf{x}\mid\mathbf{y}) \propto p_\theta(\mathbf{x})r(\mathbf{x},\mathbf{y})$, where $r$ is a constraint function depending on an auxiliary variable $\mathbf{y}$, is generally intractable. We propose to amortize the cost of sampling from such posterior distributions with diffusion models that sample a distribution in the noise space ($\mathbf{z}$). These diffusion samplers are trained by reinforcement learning algorithms to enforce that the transformed samples $f_\theta(\mathbf{z})$ are distributed according to the posterior in the data space ($\mathbf{x}$). For many models and constraints of interest, the posterior in the noise space is smoother than the posterior in the data space, making it more amenable to such amortized inference. Our method enables conditional sampling under unconditional GAN, (H)VAE, and flow-based priors, comparing favorably both with current amortized and non-amortized inference methods. We demonstrate the proposed outsourced diffusion sampling in several experiments with large pretrained prior models: conditional image generation, reinforcement learning with human feedback, and protein structure generation.

Diffusion models have emerged as effective distribution estimators in vision, language, and reinforcement learning, but their use as priors in downstream tasks poses an intractable posterior inference problem. This paper studies amortized sampling of the posterior over data, $\mathbf{x}\sim p^{\rm post}(\mathbf{x})\propto p(\mathbf{x})r(\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\mathbf{x})$ and a black-box constraint or likelihood function $r(\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning.

We study the problem of training diffusion models to sample from a distribution with a given unnormalized density or energy function. We benchmark several diffusion-structured inference methods, including simulation-based variational approaches and off-policy methods (continuous generative flow networks). Our results shed light on the relative advantages of existing algorithms while bringing into question some claims from past work. We also propose a novel exploration strategy for off-policy methods, based on local search in the target space with the use of a replay buffer, and show that it improves the quality of samples on a variety of target distributions. Our code for the sampling methods and benchmarks studied is made public at https://github.com/GFNOrg/gfn-diffusion as a base for future work on diffusion models for amortized inference.

Spurious correlations in the data, where multiple cues are predictive of the target labels, often lead to a phenomenon known as simplicity bias, where a model relies on erroneous, easy-to-learn cues while ignoring reliable ones. In this work, we propose an ensemble diversification framework exploiting Diffusion Probabilistic Models (DPMs) for shortcut bias mitigation. We show that at particular training intervals, DPMs can generate images with novel feature combinations, even when trained on images displaying correlated input features. We leverage this crucial property to generate synthetic counterfactuals to increase model diversity via ensemble disagreement. We show that DPM-guided diversification is sufficient to remove dependence on primary shortcut cues, without a need for additional supervised signals. We further empirically quantify its efficacy on several diversification objectives, and finally show improved generalization and diversification performance on par with prior work that relies on auxiliary data collection.

Spurious correlations in the data, where multiple cues are predictive of the target labels, often lead to shortcut learning phenomena, where a model may rely on erroneous, easy-to-learn, cues while ignoring reliable ones. In this work, we propose an ensemble diversification framework exploiting the generation of synthetic counterfactuals using Diffusion Probabilistic Models (DPMs). We discover that DPMs have the inherent capability to represent multiple visual cues independently, even when they are largely correlated in the training data. We leverage this characteristic to encourage model diversity and empirically show the efficacy of the approach with respect to several diversification objectives. We show that diffusion-guided diversification can lead models to avert attention from shortcut cues, achieving ensemble diversity performance comparable to previous methods requiring additional data collection.

Deep neural networks (DNNs) often rely on easy-to-learn discriminatory features, or cues, that are not necessarily essential to the problem at hand. For example, ducks in an image may be recognized based on their typical background scenery, such as lakes or streams. This phenomenon, also known as shortcut learning, is emerging as a key limitation of the current generation of machine learning models. In this work, we introduce a set of experiments to deepen our understanding of shortcut learning and its implications. We design a training setup with several shortcut cues, named WCST-ML, where each cue is equally conducive to the visual recognition problem at hand. Even under equal opportunities, we observe that (1) certain cues are preferred to others, (2) solutions biased to the easy-to-learn cues tend to converge to relatively flat minima on the loss surface, and (3) the solutions focusing on those preferred cues are far more abundant in the parameter space. We explain the abundance of certain cues via their Kolmogorov (descriptional) complexity: solutions corresponding to Kolmogorov-simple cues are abundant in the parameter space and are thus preferred by DNNs. Our studies are based on the synthetic dataset DSprites and the face dataset UTKFace. In our WCST-ML, we observe that the inborn bias of models leans toward simple cues, such as color and ethnicity. Our findings emphasize the importance of active human intervention to remove the inborn model biases that may cause negative societal impacts.