Meta AI Unveils Adjoint Sampling: Scalable Generative Modeling Without Data

Overcoming Data Scarcity in Generative Models

Generative models usually depend on large, high-quality datasets to create samples that closely mimic the original data distribution. In specialized fields such as molecular modeling or physics-based inference, obtaining such datasets is often computationally prohibitive or impossible. Instead of direct data, only a scalar reward—commonly derived from a complex energy function—is available to evaluate the quality of generated samples. This raises a critical question: how can generative models be effectively trained without direct data supervision?

Introducing Adjoint Sampling by Meta AI

Meta AI addresses this challenge with Adjoint Sampling, an innovative learning algorithm that trains generative models using only scalar reward signals. Rooted in stochastic optimal control (SOC) theory, Adjoint Sampling frames training as an optimization problem over a controlled diffusion process. Unlike traditional generative models, it requires no explicit data. Instead, it iteratively improves samples based on a reward function, often derived from physical or chemical energy models.

Adjoint Sampling is particularly effective when only an unnormalized energy function is accessible. It generates samples aligned with the target distribution dictated by this energy, eliminating the need for computationally expensive corrective methods like importance sampling or Markov Chain Monte Carlo (MCMC).

Technical Foundations of Adjoint Sampling

The core of Adjoint Sampling is a stochastic differential equation (SDE) that describes how sample trajectories evolve over time. The algorithm learns a control drift function u(x, t) that guides these trajectories so that their final states approximate a desired distribution such as the Boltzmann distribution. A novel component is the Reciprocal Adjoint Matching (RAM) loss function, which enables gradient updates using only the initial and final states of trajectories, avoiding backpropagation through the entire diffusion path and thus enhancing computational efficiency.

Sampling starts from a known base process and conditions on terminal states to build a replay buffer containing samples and gradients. This approach allows multiple optimization steps per sample in an on-policy training framework, delivering scalability that surpasses prior methods. This makes Adjoint Sampling particularly suitable for high-dimensional problems like molecular conformer generation.

The algorithm also supports geometric symmetries and periodic boundary conditions, ensuring that models respect molecular invariances such as rotation, translation, and torsion. These capabilities are vital for generating physically meaningful molecular structures in chemistry and physics.

Performance Highlights and Benchmark Achievements

Adjoint Sampling delivers state-of-the-art performance on both synthetic and real-world benchmarks. For synthetic tasks like Double-Well (DW-4) and Lennard-Jones potentials (LJ-13 and LJ-55), it significantly outperforms baselines such as DDS and PIS, particularly in energy efficiency. For instance, where DDS and PIS require 1000 energy evaluations per gradient step, Adjoint Sampling achieves similar or better results with only three evaluations, measured by metrics like Wasserstein distance and effective sample size (ESS).

In practical applications, the algorithm was tested on large-scale molecular conformer generation using the eSEN energy model trained on the SPICE-MACE-OFF dataset. The Cartesian variant of Adjoint Sampling with pretraining reached up to 96.4% recall and 0.60 Å mean RMSD, outperforming RDKit ETKDG, a widely used chemistry baseline, across all metrics. It also generalized effectively to the GEOM-DRUGS dataset, showing improved recall while maintaining competitive precision.

The method’s stochastic initialization and reward-based learning enable broad exploration of configuration space, producing diverse conformers essential for drug discovery and molecular design.

Transforming Reward-Driven Generative Modeling

Adjoint Sampling marks a significant advance in generative modeling without reliance on data. By utilizing scalar reward signals and an efficient on-policy training method grounded in stochastic control theory, it enables scalable training of diffusion-based samplers with minimal energy evaluations. Its support for geometric symmetries and broad generalization make it a foundational tool in computational chemistry and related fields.