Proteins are essential for almost all biological processes and derive their diverse functions from complex $3 \rm D$ structures, which are in turn determined by their amino acid sequences. In this paper, we exploit the rich biological inductive bias of amino acid sequences and introduce FoldFlow++, a novel sequence-conditioned $\text{SE}(3)$-equivariant flow matching model for protein structure generation. FoldFlow++ presents substantial new architectural features over the previous FoldFlow family of models including a protein large language model to encode sequence, a new multi-modal fusion trunk that combines structure and sequence representations, and a geometric transformer based decoder. To increase diversity and novelty of generated samples -- crucial for de-novo drug design -- we train FoldFlow++ at scale on a new dataset that is an order of magnitude larger than PDB datasets of prior works, containing both known proteins in PDB and high-quality synthetic structures achieved through filtering. We further demonstrate the ability to align FoldFlow++ to arbitrary rewards, e.g. increasing secondary structures diversity, by introducing a Reinforced Finetuning (ReFT) objective. We empirically observe that FoldFlow++ outperforms previous state-of-the-art protein structure-based generative models, improving over RFDiffusion in terms of unconditional generation across all metrics including designability, diversity, and novelty across all protein lengths, as well as exhibiting generalization on the task of equilibrium conformation sampling. Finally, we demonstrate that a fine-tuned FoldFlow++ makes progress on challenging conditional design tasks such as designing scaffolds for the VHH nanobody.

We explore the application of a nonlinear MCMC technique first introduced in [1] to problems in Bayesian machine learning. We provide a convergence guarantee in total variation that uses novel results for long-time convergence and large-particle (``propagation of chaos'') convergence. We apply this nonlinear MCMC technique to sampling problems including a Bayesian neural network on CIFAR10.