Where the Diversity Is Injected: Conditioning, Trajectory, and Latent Loci in Training-Free Ensemble Sampling

Question: How do inference-time sampling strategies for generative protein structure models diversify conformational ensembles without retraining, and how do repulsion- or diversity-based guidance methods compare?

Answer

Across the retrieved work, inference-time diversification is not one mechanism but a family of interventions at three distinct loci — the conditioning signal, the denoising trajectory, and the latent or embedding representation — all of which exploit the fact that pretrained structure generators already encode alternative conformations that default inference fails to expose. Repulsion- and diversity-based guidance methods occupy the trajectory locus: they convert otherwise independent parallel samples into an interacting particle system, driving samples apart either in output coordinate space or in internal feature space, and they are the most consistently effective single class for recovering states that default sampling misses. Taken together, the papers support a sharper comparative claim than "repulsion works": repulsion guidance whose objective is explicit and physically grounded (an experimental likelihood, a force-field prior, a collective-variable bias with reweighting, or a derived Doob-transform target) improves coverage and validity jointly, whereas bare heuristic repulsion buys coverage with measurable physical degradation and, in most deployments, an uncontrolled target distribution. The field therefore has a validated diversity mechanism but no validated equivalence between its variants, and no shared benchmark on which they can be ranked.

Repulsion guidance works by converting independent samples into an interacting particle system, and the locus of application determines what it can diversify

Repulsion at the level of predicted coordinates is the simplest instantiation: interpreting AF3's diffusion module as a stochastic sampling process analogous to MD, a repulsive biasing potential between predicted structures explores a wider conformational space and recovers ligand-bound states of motor and transporter proteins that unmodified AF3 does not capture [3]. Applying the repulsion earlier, to Boltz-2's trunk single and pair embeddings via a pairwise C-RMSD repulsion gradient, means the updated trunk conditions every subsequent denoising step while leaving weights untouched [14]. Repulsion can also be formulated as a meta-energy biasing layer on top of a pretrained diffusion model, with inter-sample repulsion offered as one of three exploration modes alongside optimisation and steering to user-specified targets [8]. A history-dependent variant makes the bias memory-aware rather than batch-aware, using a distance-weighted term that steers reverse-time sampling away from previously generated structures, regularised by an environment-support term and followed by score-based re-projection onto the data manifold [9]. Repulsion need not act on structure at all: a repulsive potential centred on low-dimensional collective variables of recent samples pushes future samples toward novel CV regions and effectively raises temperature in the projected space [25]. The non-repulsion diversity objectives at the same locus are entropy- and variance-based, learning modifications to AlphaFold2's intermediate hidden states under a negative entropy loss [13] or targeting an explicitly specified variance-weighted batch distribution whose sampler follows as a Doob h-transform [24].

Steered repulsion reliably widens coverage on the benchmarks its authors choose, and the gains are largest on states default sampling cannot reach

ConforFlux improves per-state success over default Boltz-2 by 3–17 percentage points across four conformational-change categories and also improves coverage on OpenFold3 and Protenix, sampling inward-facing human dopamine transporter conformations absent from 500 default samples [14]. The history-dependent generative-space bias raises diversity by 35% on DynamicPDB-80 and reaches the unbiased emulator's coverage up to roughly 15× faster on zero-shot fast-folding proteins, rising to roughly 37× with refinement while covering about 3× as many low-energy states [9]. GNMCADS, which anneals the conditioning signal guided by a Gaussian network model of intrinsic dynamics rather than repelling samples, reports improved sampling diversity against other current conformational sampling methods across 92 proteins including 54 class A GPCRs and 23 proteins with major domain movements [1]. AF3-ReD additionally reports that, relative to an MSA-based strategy, its repulsion produced intermediate conformations closer to the stable states [3]. Collective-variable repulsion recovers diverse conformational states and accurate free energy profiles on peptide benchmarks and enables reweighting to retain sampling from the approximate Boltzmann distribution [25].

Bare repulsion buys coverage with measurable physical cost, whereas guidance with an explicit target improves diversity and validity together

The clearest evidence of a trade-off is that the same procedure reporting 3–17 point success gains also reports increased clashscores [14]. Against this, ConforMix combines classifier guidance, filtering, and free energy estimation and captures domain motion, cryptic pocket flexibility, and transporter cycling while avoiding unphysical states [5]. Optimising over latent representations to maximise ensemble log-likelihood removes dependence on diffusion length and initialization bias and, by combining AlphaFold3 priors with force-field priors, improves diversity, physical energy, and experimental agreement simultaneously, consistently outperforming state-of-the-art guidance on X-ray and NMR data [7]. Metadiffusion's biasing layer, evaluated empirically, yields residue-level flexibility patterns that closely match MD simulations and ensembles consistent with SAXS and NMR chemical shifts without retraining [8]. A Gibbs-style reformulation makes the distinction explicit: variance-tilted sampling derives the sampler as the Doob h-transform of independent diffusion dynamics, yielding an interaction term that repels posterior denoised means plus a curvature term, and its authors present this as a transparent probabilistic target "rather than a heuristic repulsive drift" [24]. Thermodynamic framing offers the same lesson from the other direction, with minimum-excess-work guidance aligning generated distributions to experimental observables while preserving entropy [10].

Conditioning-side and latent-side interventions are complementary to trajectory steering rather than substitutes for it

Combining a secondary-structure-conditioned retrained OpenFold with AlphaFlow improved conformer recovery beyond either alone, with the combined framework retaining the complementary strengths of both approaches [16]. That same study found its conditioning-based approach recovered both conformers in 84% of cases at TM-score ≥ 0.8, above AlphaFlow's 75.4% and above MSA-clustering [16], which contests the simpler reading that MSA subsampling is the default diversity lever. A frustration-guided subsampling scheme reaching up to +15.5 percentage points on allosteric systems nonetheless attributes its advantage largely to the effective depth of selected subsets under matched-depth controls, recasting MSA subsampling as representation-guided reweighting rather than a distinct diversity mechanism [21]. Plain shallow MSA subsampling combined with randomised alanine scanning expands predicted apo/holo ensemble diversity but still predicts the most stable domain orientation for large hinge-like motions [17]. Latent-space routes sidestep sampling schedules entirely: ADAM optimisation in ESMFold embedding space needs no retraining and adapts to diverse restraint conditions [12], adversarial latent flooding recovers experimental structural fluctuations and cryptic binding sites [20], parallel tempering in ESM3's discrete structure-token space crosses barriers that base generative models cannot [19], and structure language modelling explores diverse ensemble modes 20–100× faster than existing methods [4]. Guidance applied in a coarse latent space can also trade designability against diversity deliberately rather than incidentally [2], which supports the broader review categorisation of fixed-parameter steering strategies as condition-then-sample rather than weight-modifying [11].

Conflicts and gaps

The central disagreement is whether the diversified ensemble is a reweighting of the correct distribution or merely a broader one. Collective-variable repulsion explicitly reweights to retain Boltzmann sampling [25], the latent-optimisation framework reports Boltzmann-weighted ensembles [7], and metadiffusion's flexibility patterns match MD [8]; yet the variance-tilted analysis characterises general repulsive drift as heuristic with no specified target [24], and clashscore inflation is documented for at least one repulsion scheme [14]. Second, it remains contested whether recovered states reflect genuine extrapolation or training-set recall: reviews argue AlphaFold-based predictors over-rely on their training set and produce degenerate high-confidence alternative-fold predictions [18], and that ensembles are predicted by association with training-set structures [15]; post-training-cutoff target tests are the only direct counter-evidence retrieved [14]. Third, no head-to-head comparison exists — GNMCADS uses 92 proteins [1], ConforFlux four categories on three models [14], the implicit-bias work 12 fast folders [9], SF-Cluster 48 cases [21], and MSFold 313 pairs [19], so cross-method claims are untested. Fourth, gains may not transfer across sampler classes: diffusion converges by pronounced late-stage stochastic relaxation and robustly recovers configurational breadth, while rectified flow depends far more strongly on architectural expressivity [6]. Fifth, evaluation itself is compromised — perturbing AlphaFold3 embeddings to maximise ipTM artificially inflates model confidence [7], and a population of bespoke diversity and ensemble-quality metrics has appeared without cross-validation against each other [19] [22].

What would change the answer

A shared benchmark that fixes seed count and wall-clock budget and scores coverage, Boltzmann-weighted observables, and physical validity on the same targets would settle whether repulsion's clashscore cost is intrinsic or a tuning artifact; the ATLAS-style distributional metrics plus OpenMM energies already exist as components [23] [6]. A decisive test of whether guided ensembles are reweightings of the base distribution would couple any repulsion scheme to the reweighting machinery already demonstrated for CV-space bias [25] and the entropy-preserving machinery of observable guidance [10]. Matching the number of independent samples to the number of particles would isolate diversity attributable to repulsion from diversity attributable to sampling more, a control that the matched-depth analysis in MSA subsampling shows is decisive [21]. Extending post-release target splits beyond one study [14] to every reported method would resolve the training-set-recall objection [18]. Finally, an interacting-particle sampler with a derived Doob target [24] benchmarked against heuristic repulsion under identical compute would answer whether the heuristic is an approximation of something principled or a different objective entirely.

References

[1] Uzum, A. S., Haliloglu, T.. "GNMCADS: Sampling For Protein Conformation Diversity With Gaussian Network Model Guided Condition Annealed Diffusion Sampler". bioRxiv. 2026-09-01T00:00:00.000Z. URL: https://doi.org/10.64898/2026.08.28.747885

[2] Jason Yim, Marouane Jaakik, Ge Liu, Jacob Gershon, Karsten Kreis, David Baker, Regina Barzilay, Tommi Jaakkola. "Hierarchical protein backbone generation with latent and structure diffusion". arxiv. 2025-04-15T00:00:00.000Z. URL: https://arxiv.org/abs/2504.09374

[3] Ohnuki, J., Okazaki, K.-i.. "Enhanced sampling of protein conformations in AlphaFold3 with repulsive bias in the diffusion generative model". bioRxiv. 2025-12-18T00:00:00.000Z. URL: https://doi.org/10.64898/2025.12.17.693105

[4] Jiarui Lu, Xiaoyin Chen, Stephen Zhewen Lu, Chence Shi, Hongyu Guo, Yoshua Bengio, Jian Tang. "Structure Language Models for Protein Conformation Generation". arxiv. 2025-03-14T00:00:00.000Z. URL: https://arxiv.org/abs/2410.18403

[5] Daniel D. Richman, Jessica Karaguesian, Carl-Mikael Suomivuori, Ron O. Dror. "Unlocking hidden biomolecular conformational landscapes in diffusion models at inference time". arxiv. 2026-02-05T00:00:00.000Z. URL: https://arxiv.org/abs/2512.03312

[6] B E, N., Mondal, J.. "How Generative Models Approach Molecular Conformational Sampling". bioRxiv. 2026-04-14T00:00:00.000Z. URL: https://doi.org/10.64898/2026.04.10.717851

[7] Advaith Maddipatla, Anar Rzayev, Marco Pegoraro, Martin Pacesa, Paul Schanda, Ailie Marx, Sanketh Vedula, Alex M. Bronstein. "Inference-time optimization for experiment-grounded protein ensemble generation". arxiv. 2026-06-30T00:00:00.000Z. URL: https://arxiv.org/abs/2602.24007

[8] Lam, H. Y. I., Pujalte Ojeda, S., Brezinova, M., Hanke, J., Ong, X. E., Mu, Y., Vendruscolo, M.. "Metadiffusion: inference-time meta-energy biasing of biomolecular diffusion models". bioRxiv. 2026-02-11T00:00:00.000Z. URL: https://doi.org/10.64898/2026.02.10.704873

[9] Kaihui Cheng, Zhiqiang Cai, Wenkai Xiang, Zhihang Hu, Siyu Zhu, Tzuhsiung Yang, Yuan Qi. "Learning Implicit Bias in Generative Spaces for Accelerating Protein Dynamics Emulation". arxiv. 2026-10-09T00:00:00.000Z. URL: https://arxiv.org/abs/2606.01833

[10] Christopher Kolloff, Tobias Höppe, Emmanouil Angelis, Mathias Jacob Schreiner, Stefan Bauer, Andrea Dittadi, Simon Olsson. "Minimum-Excess-Work Guidance". arxiv. 2025-05-26T00:00:00.000Z. URL: https://arxiv.org/abs/2505.13375

[11] Filippo Stocco, Michele Garibbo, Noelia Ferruz. "Steering Generative Models for Protein Design: Aligning and Conditioning Strategies". arxiv. 2026-02-27T00:00:00.000Z. URL: https://arxiv.org/abs/2511.21476

[12] Yu, Z., Liu, Y., Lin, G., Jiang, W., Chen, M.. "ESMAdam: a plug-and-play all-purpose protein ensemble generator". bioRxiv. 2025-01-21T00:00:00.000Z. URL: https://doi.org/10.1101/2025.01.19.633818

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[14] Suzuki, S., Amagasa, T.. "ConforFlux: Particle-Guided Trunk Repulsion for Diverse Protein Conformations". bioRxiv. 2026-10-19T00:00:00.000Z. URL: https://doi.org/10.64898/2026.05.16.725138

[15] Myeongsang Lee, Lauren L. Porter. "Fold-switching proteins push the boundaries of conformational ensemble prediction". arxiv. 2026-01-09T00:00:00.000Z. URL: https://doi.org/10.1146/annurev-biodatasci-092524-114822

[16] Syrlybaeva, R., Strauch, E.-M.. "ConforFold Recovers Alternative Protein Conformations Beyond MSA Subsampling". bioRxiv. 2025-10-14T00:00:00.000Z. URL: https://doi.org/10.1101/2025.10.14.682366

[17] Raisinghani, N., Parikh, V., Foley, B., Verkhivker, G.. "Assessing Structures and Conformational Ensembles of Apo and Holo Protein States Using Randomized Alanine Sequence Scanning Combined with Shallow Subsampling in AlphaFold2 : Insights and Lessons from Predictions of Functional Allosteric Conformations". bioRxiv. 2024-11-06T00:00:00.000Z. URL: https://doi.org/10.1101/2024.11.04.621947

[18] Devlina Chakravarty, Myeongsang Lee, Lauren L. Porter. "Proteins with alternative folds reveal blind spots in AlphaFold-based protein structure prediction". arxiv. 2024-10-22T00:00:00.000Z. URL: https://arxiv.org/abs/2410.14898

[19] Wang, Z., Yu, Y., Zheng, W.-M., Yu, C., Bu, D.. "Sampling in structure-token space enables accurate prediction of multiple protein conformations". bioRxiv. 2026-09-09T00:00:00.000Z. URL: https://doi.org/10.64898/2026.03.03.708411

[20] QIAN, R., Zhan, R., Song, Z., Huang, J.. "Zero-Shot Generation of Protein Conformational Ensembles Through AlphaFold Latent Flooding". bioRxiv. 2026-04-27T00:00:00.000Z. URL: https://doi.org/10.64898/2026.04.16.718914

[21] Hanqun Cao, Zijun Gao, Chunbin Gu, Ge Liu, Pheng Ann Heng, Pranam Chatterjee. "SF-Cluster: Frustration-Guided MSA Subsampling for Alternative Protein Conformation Recovery". arxiv. 2026-07-02T00:00:00.000Z. URL: https://arxiv.org/abs/2607.0018

[22] Yuda Bi, Huaiwen Zhang, Jingnan Sun, Vince D Calhoun. "Spectral Coherence Index: A Model-Free Metric for Protein Structural Ensemble Quality Assessment". arxiv. 2026-03-30T00:00:00.000Z. URL: https://arxiv.org/abs/2603.2588

[23] Yang, X., Cui, X., LI, X., Hou, D., Wang, S., Xie, T., Zhang, G.. "TopoFlow: Evolutionarily Conditioned Flow Matching for Protein Conformational Ensemble Generation". bioRxiv. 2026-09-24T00:00:00.000Z. URL: https://doi.org/10.64898/2026.09.22.753441

[24] Iskander Azangulov, Leo Zhang, Kianoosh Ashouritaklimi. "Variance-Tilted Diffusion Models for Diverse Sampling". arxiv. 2026-06-23T00:00:00.000Z. URL: https://arxiv.org/abs/2606.22239

[25] Juno Nam, Bálint Máté, Artur P. Toshev, Manasa Kaniselvan, Rafael Gómez-Bombarelli, Ricky T. Q. Chen, Brandon Wood, Guan-Horng Liu, Benjamin Kurt Miller. "Enhancing Diffusion-Based Sampling with Molecular Collective Variables". arxiv. 2026-02-18T00:00:00.000Z. URL: https://arxiv.org/abs/2510.11923

How this survey was made

This survey answers one question: “How do inference-time sampling strategies for generative protein structure models diversify conformational ensembles without retraining, and how do repulsion- or diversity-based guidance methods compare?”

We keep our own collection of recent preprints and refresh it every day from bioRxiv, medRxiv, arXiv, PsyArXiv, SocArXiv and ChemRxiv. For each survey, we search that collection for recent work and keep the strongest matches: papers that use the same terms as the question, and papers on the same topic in different words.

The text was written from the titles and abstracts of those papers; the full texts were not read. Statements that draw on a particular paper are marked with a number in brackets. The reference list just above is the 25 papers whose work this text draws on, chosen from the 108 papers those searches returned; the rest of the shortlist is not printed. It is not a complete review of everything published on the question.

Treat this as a starting point and a reading list, not a peer-reviewed review. The searches behind this survey ran on October 21, 2026 and covered work from the previous two years.