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Christopher Kolloff, Tobias Höppe, Emmanouil Angelis, Mathias Jacob Schreiner, Stefan Bauer, Andrea Dittadi, Simon Olsson, Minimum-Excess-Work Guidance, https://arxiv.org/abs/2505.13375v3

Authors of the review

Giovanni Bussi, Olivier Languin-Cattoën

This report was written after a journal club given by Giovanni Bussi in the bussilab group meeting. All the members of the group, including external guests, are acknowledged for participating in the discussion and providing feedback that was useful to prepare this report.

The corresponding authors of the original manuscript were consulted before posting this report.

Summary

The authors present two new approaches to guide score-based diffusion models so as to modulate the resulting ensembles. In one of them, experimental data (in the form of ensemble averages) are enforced. In the other one, sampling is enriched in conformations from a preassigned region in the conformational space (e.g., from the transition state).

Comments

• The authors introduce both an SDE (Eq. 3) and an ODE (Eq. 4). In the Path guidance part they claim that the SDE was more robust. Could they clarify if they observed the same in the Observable guidance part?

• In the definition of Work (Eq. 11) it looks like the authors compute the projection of the guiding force (-g^2/2h) on the displacement induced by the force itself (-g^2/2h*dt). Why isn't the projection of the guiding force on the full displacement (including f and s) considered? Is it an empirical choice? Or is there some intuition?

• In Eq. (15) the Lagrangian multipliers are said to be pre-estimated. Are they estimated using a sample from the original (unguided) diffusion model? If so, are they suffering of the usual problem of reweighting methods, that is the fact that if the overlap between the initial ensemble and the experimental one is too low the estimation might be very poor?

• Again in Eq. (15): did we understand correctly that the authors are only learning the schedule η(t)? As far as we understood, in both the presented examples M=1. With large values of M, do the authors expect that learning a single prefactor would be sufficient? In other words: in high dimensionality, if the estimated vector of lambda is noisy, do the authors expect that adjusting the learning schedule is sufficient? Related to this point, in Section 6 the authors report as a limitation that "scalability has been demonstrated in moderate settings." We would suggest to recall here that only the case M=1 was considered (if we understood correctly the results). Perhaps a comment on what the authors expect when M>1 would be useful.

• In Eq. (18), we believe N is not defined.

• In Fig. (9), there might be a plotting mistake in the lower panels. The range seems to be inconsistent with the one used in Fig. (2).

• In Fig (9), right panel: is there an intuitive explanation for the peak close to x=0

• We were a bit confused by the description of the observable used in the Prinz potential. Is it identical to the ground truth distribution?

• Fig (3), the color legend is not very clear. Does it refer to panel (A), (B), or both?

• In Section 4.1.2, "experimental setup": the authors used Delta G = -kBT log (pfolded/punfolded) as an observable. However, this is technically not an ensemble average. Does this imply that they are modifying Eq. (16) to cover this case? In addition: if the experimental observable is only related to the folded and unfolded populations (as defined by the vertical dashed line in Fig. 3B), it is a bit surprising that the red minimum is shifted to the left when compared to the blue one, in Fig 3B. This would be expected if the authors were enforcing the average value of the end to end distance.

• In Section 4.1.2, "evaluation" there is a typo in units, or perhaps "mean squared error" should be replaced with "root mean squared error".

• In Section 4.1.2. "evaluation", it is not clear why after guidance the D_KL with respect to MD is decreased. Is this expected? Which was the population of the native state in the MD simulations used to train the diffusion model? In other words, our understanding is that agreement with experiment should improve thanks to guidance. But we are not sure to understand why agreement with MD simulations should improve.

Competing interests

The authors declare that they have no competing interests.