reviews: 
Comments: This work extends Multiflow to accept spatial conditioning of secondary structures via 3D ellipsoids, aiming to improve control in protein generation and reduce the overrepresentation of alpha-helices in current generative models. Building on Multiflow’s architecture, the authors address two main challenges:

1. Integrating and updating ellipsoid conditioning with structure embeddings with minimal modifications: they introduced an *Invariant Cross Attention* module to update residue embeddings while preserving local SE3 invariance.
2. Implementing an effective conditioning approach for flow-matching models: they used classifier-free guidance to interpolate flow vectors across translation, rotation, and amino acid spaces, and employ self-conditioning to refine predicted structures
    
Extensive experiments show that the proposed model can faithfully follow spatial conditioning, resulting in greater diversity, novelty, and improved secondary structure composition. This improves Multiflow by generating proteins with secondary structures more similar to natural proteins. 
Overall, this work presents a straightforward approach to control protein generation, enhancing Multiflow's diversity, novelty, and secondary structure accuracy.
Strengths: **[Clarity & Quality]**
- The manuscript is well-written, with a thorough introduction and background information on protein structure generation, spatial conditioning, and flow matching for data generation. Overall, it provides a smooth reading experience.
- The paper is of good quality, presenting clear mathematical foundations grounded in current techniques for protein modeling, diffusion-based generation, and guided sampling.
- The problem is well-defined, and the authors designed several experiments to evaluate model performance in 1) following conditioning, 2) improving general performance, and 3) demonstrating practical use in flexible conditioning, with both quantitative and qualitative comparisons.

**[Significance]**
- The spatial conditioning approach using ellipsoids is intuitive for practical applications and has potential implications for the utility of protein generation models.
- The proposed methods appear generalizable to various spatial conditioning scenarios. (*However, this paper focuses solely on secondary-structure conditioning.*)

**[Originality]**
- The authors introduce a novel conditioning modality using spatial ellipsoids for protein generation, along with a new layer, "invariant cross-attention," to integrate this information.
Weaknesses: **[Clarity]**
- Some design choices and model details lack clear explanations or in-depth examination (see Q1, 2, and 4).

**[Soundness]**
- Performance on Natural Proteins: While the authors demonstrate high designability at fixed helicity levels on synthetic data, it isn't as clear if these benefits hold for natural proteins (see Q3).

**[Significance]**
- Scope: The current methods are examined only on Multiflow and for secondary structure guidance. Their practical impact on other protein generation models and types of spatial conditioning (e.g., domains, hydrophobic cores) is not extensively explored.
Recommendation: 8
Reviewer confidence: 3
Soundness/correctness: 3
Clarity: 4