La-Proteina: Atomistic Protein Generation via Partially Latent Flow Matching
Authors: Tomas Geffner
Kieran Didi
Zhonglin Cao
Danny Reidenbach
Zuobai Zhang
Christian Dallago
Emine Kucukbenli
Karsten Kreis
Arash Vahdat
Venue: ICLR 2026 Poster (2026)
Keywords: Atomistic protein design
flow matching
latent diffusion
motif scaffolding
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
TL;DR: We introduce a partially latent flow matching model for atomistic protein design.

Abstract: Recently, many generative models for de novo protein structure design have emerged. Yet, only few tackle the difficult task of directly generating fully atomistic structures jointly with the underlying amino acid sequence. This is challenging, for instance, because the model must reason over side chains that change in length during generation. We introduce La-Proteina for atomistic protein design based on a novel partially latent protein representation: coarse backbone structure is modeled explicitly, while sequence and atomistic details are captured via per-residue latent variables of fixed dimensionality, thereby effectively side-stepping challenges of explicit side-chain representations. Flow matching in this partially latent space then models the joint distribution over sequences and full-atom structures. La-Proteina achieves state-of-the-art performance on multiple generation benchmarks, including all-atom co-designability, diversity, and structural validity, as confirmed through detailed structural analyses and evaluations. Notably, La-Proteina also surpasses previous models in atomistic motif scaffolding performance, unlocking critical atomistic structure-conditioned protein design tasks. Moreover, La-Proteina is able to generate co-designable proteins of up to 800 residues, a regime where most baselines collapse and fail to produce valid samples, demonstrating La-Proteina's scalability and robustness.

Published as a conference paper at ICLR 2026
LA-PROTEINA: ATOMISTIC PROTEIN GENERATION VIA PARTIALLY LATENT FLOW MATCHING
Tomas Geffner' Kieran Didi
Zhonglin Cao
Danny Reidenbach'
Zuobai Zhang
Christian Dallago' Emine Kucukbenli
Karsten Kreis"
Arash Vahdat
NVIDIA
Uniivrriity of Oxford
Mila - Québec Al Institute
Univerriteé de Montréal
Project page:
ABSTRACT
While many generative models for protein design have emerged, few tackle the difficult task of jointly generating full-atom structures and their corresponding sequences, a challenge compounded by sequence-dependent side-chain dimen- sionality. We introduce La-Proteina for atomistic protein design based on a novel partially latent representation; the protein backbone is modeled explicitly, while sequence and all other atomistic details are captured in per-residue latent variables of fixed size. Flow matching in this partially latent space then models the joint distribution over sequences and full-atom structures. La-Proteina achieves state-of-the-art performance on key generation benchmarks, including all-atom co-designability, diversity, and structural validity. Notably, it also surpasses previous models in atomistic motif scaffolding, unlocking critical structure-conditioned design tasks. Moreover, La- Proteiin generates co-designable proteins of up 800 residues, regime where most baselines collapse or fail produce valid samples, demonstrating its unique scalability and robustness.
INTRODUCTION
The design of novel proteins with specific structures and functions has immense potential in various fields (Richardson & Richardson 1989 Huang et al., 2016 Kuhlman & Bradley 2019). A challenge in de novo protein design capturing the relationship between protein sequence and structure. Most existing methods decouple these aspects, generating sequences that are later folded (Wang et al.) 2024b) or designing backbones that are subsequently sequenced (Watson et al., 2023). However, accurately modeling the joint distribution over sequences and fully atomistic structures could unlock fine-grained control over functional sites and enable key protein design tasks, such as atomistic motif' scaffolding. This problem is made inherently difficult by the need to handle both discrete sequences and continuous coordinates, along with the sequence-dependeen Recent methods tackling this problem learn generative models directly in data space (Qu al.) 2024] Chu et al.) (004)), though these often struggle with modeling accuracy and scalability. Other approaches use latent representations (Lu al., 2024 Fu et al., 22024) McPartlon al.) [0244] Yim et al. 2025) but often fail to deliver competitive performance despite their conceptual appeal (Sec. 4).
dimensionality of side chains.
We introduce La-Proteina (Latent Proteina), a method for atomistic protein design based on partially latent flow matching, combining the strengths of explicit and latent modeling. La-Proteina models the a-carbon coordinates explicitly, while capturing sequence and coordinates of all non-a-carbon atoms within a continuous, fixed-size latent representation per residue. We first train Variational Autoencoder (VAE) (Kingma al. 2013) Rezende al. 2014). encoding sequence and side chain details in latent space, followed by flow matching model (Lipman et al. 2023) that jointly generates o-carbon coordinates and latent variables. New proteins are generated by sampling the flow model and decoding the a-carbons and latent variables into sequences and fully atomistic structures (Fig, [
La- ProPrriiin's partially latent approach shifts the core learning problem from a mixed dis- crete-continuous space with variable dimensionality to per-residue, continuous space of fixed dimen- sionality, making it amenable to powerful used generative modeling techniques such as flow matching.
Equul contribution 'equal advising.

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Encoder
abte, Cy
encoding
Decoder
Fully Atomiktii
Pen-Seechae sation
Per Residec
Bucisonn
Aigha-Carbon
Gemenntion
Backoone Stracture
Reconstructed Generate atedd Fully Atomiistcc Protain
Perriall latenz Flow Marching
Denoiser
Parddesidur
Per Caulde
Training: Decoder
Per Rajidue
Partially Latent Flow Training: (Frozen) Encoder Joint Denpiser
Genverstion Floss
Generation: (Frozen) Joint
Decoder
Figure I: La-Proteina consists of encoder 9u (a), decoder Pe (b), and joint denoiser pe (c). The encoder fea- turizes input protein and predicts per-residue latent variables z of constant dimensionality. Together with underlying a-carbon backhone xc.: the decoder outputs sequence s and all other atoms x Cc. and reconstructs the atomistic protein. To facilitate generation of de novo proteins, a partially latent flow model jointly generates novel c-carbon backbone structures xc., and latents The model is trained in two stages and all networks implemented leveraging the transformer architecture (Geflner al. 2025 details Sec. 3
Meanwhile, maintaining the explicit separation of the a-carbon coordinates and the latent variables allows greater flexibility during generation. In particular, it enables the structural scaffold and the remaining atomic details to be generated using different generation schemes, i.e., different discretiza- tion schedules to simulate the underlying generative stochastic differential equation. La-Proteina' s neural networks are implemented using efficient transformer architectures (Vaswani et al. (017) 7, Geffner et al. 2025), guarantecing the model's 's scalability long proteins, many model parameters, and large training data data-we we train La- Proteina on up to 46 million protein structure-scquence pairs.
model against leading publicly available methods for atomistic protein design and achieve state-of-the. of-the-art atomistic performance as measured by the all-atom co-designability and diversity metrics. La- La-Proteina can generate co-designable proteins of up 800 residues, a regime where existing models collapse or run out of memory, demonstrating our method's strong scalability. We further assess the generated structures' geometric quality through analyses of side-chain conformations and validate overall structural integrity (Davis et al.) 2007). La-Proteina significantly surpasses existing methods in these evaluations as well. Next, we apply La-Proteina to atomistic motif scaffolding, a critical task for protein engineering that most prior work has addressed only at the coarser backbone level (Watson al. 2023 Yim et al. 2024 Lin al. 2024, Geffner et al., 2025). We tackle both all-atom and tip- atom scaffolding, where in the latter case only functionally critical side chain tip atoms are given, rather than atoms the motif residues. Our model performs these tasks in two setups: the standard indexed task, where motif residue sequence indices are specified; and the more challenging unindexed task (Ahern et al.) 2025), where these sequence indices unknown. Our approach solves most benchmark tasks across all setups and outperforms baselines. We provide further insights through ablation studies and careful analysis of the model's latent space, which shows that La-Proteina encodes atomistic residue structure and amino acid type in localized and consistent manner. In conclusion, La- La-Protei represents a versatile, high-quality, fully atomistic protein structure generative model, with the potential enable new, challenging protein design tasks.
We empirically compare
Main contributions. (i) We propose La-Proteina, a partially latent flow matching framework designed for the joint generation of protein sequence and fully atomistic structure. (ii) La-Proteina achieves statc-of-the-arr performance in unconditional protein generation. (iii) We verify La- Proteina's scalability, generating diverse, co-designable and structurally valid fully atomistic proteins of up to 800 residues. (iv) We successfully apply La-Proteina to indexed and unindexed atomistic motif scaffolding, two important conditional protein design tasks. (v) We provide further insights through ablations, latent space analyses, and biophysical assessments of La- Proteinn''ss 's generated atomistic protein structures, demonstrating our model's superiority over previous all-atom generators.
PRELIMINARIES
VAEs (Kingma et al. 2013) Rezende et al. 2014) learn probabilistic representation data x within latent space employing two neural networks: encoder mapping sample distribution
2

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100
200
300
400
500
600
700
800
Figure 2: Fully atomistic La-Proteina samples. Numbers denote residue count. All samples dosigngna...e
(z x) over latent variables and decoder mapping to distribution in data space pa (x zz) VAEs are trained by maximizing the Evidence Lower Bound, ELBO(ó, eb = Ex (logz pa Px (x/z)] (T, (2|x) |l p(z)). This objective balances reconstruction quality with KI. divergence- based regularization term that pushes the learned posterior 44 x) towards an uninformative prior p(z).
2023) trains neu- ral network Vo (x(x,, () to model the velocity field vx(x) ) that transports samples from a base distribution Po the data distribution pi along probability path pt. for / [0, 1]. This path is often defined by linearly interpolating between samples x" Po and x P1 as x = -1 10--tha t)x" tx'. The denoiser network Vy is trained by minimizing the conditional flow matching objective, Er. [
Flow matching (Lipman et al. 2023 Albergo & Hunden-Eiinder 2023 Liu et al.
(x' (el-x") xx) [[ Flow matching
be applied directly in data space or in latent spaces learned by models like VAEs (Rombach et al. 2022) Vahdat et al. (2021). Furthermore, when is Gaussian, flow match- ing equivalent to diffusion models (Song et 2021; Gao al. 2025). allowing to compute the intermediate score functions Xx log Pt (x') as function of the trained network vo(x',
Protein representation. Protein data includes sequence (20 residue types) and 3D structure. Different residues share a common backbone, including the a-carbon atom, but contain distinct atoms in their side chains. The Atom37 representation defines standardized superset of 37 potential atoms per residue, which allows storing the structure of an L-residue protein as tensor of shape [I,37,3] 3]. The relevant subset of coordinates is selected based on each residue's type.
Related work. Early diffusion-based protein generators, such RFDiffusion (Watson et al. 2023 and Chroma (Ingraham et al. 2023), focused on backbone generation. This area has since diversified. with some approaches leveraging diffusions on the SO(3) manifold (Yim et al.) 2023b Bose ctt al.
2024, 2024, Huguet et al. 2024), while others employ Euclidean Flow Matching (Lin & Alquraishi
2023 Lin et al. [024| Gefffer al. 2025). ProtComposer
auxiliary statistical model and
3D primitives (Stark et al. 2025). Several works (Lin et al. 2024 Qu et al., 2024 Geffner et al.
2025) obtained good performance training on synthetic structures from the AlphaFold database
(AFDB) (Jumper et 2021 Varadi et al.) 2021). which is significantly larger than the protein databank (PDB) (Berman al. 2000). Recently, the task of eequence-structurr co-design has gained prominence. Some methods address this by jointly modeling protein backbones and sequences (Campbell et al. 2024 20.44 Ren al., 2024,) Yim et al.) (025). Others tackle fully atomistic structures. including side chains, operating either in data space (Qu et al., 2024 Chu et al.) 2024 Lisanza 2025) or via latent variable models (McPartion
al. 2023, Chen et al.
al.) 2024] Fu al.
2024 Lu et al.] 2024 Yim et al. 2025). Language models have also been used for protein design,
with some methods focusing on protein sequences (Wang et al. 2024b); others tokenize structural information and model sequence and structure jointly (Hayes et al. 2024 Wang et al. 2024c). In
this work we introduce La-Proteina for atomistic protein design and provide a thorough evaluation of its capabilities in unconditional monomer generation and motif scaffolding. Concurrent work by AAnonymous] (2025) extends La-Pret Proteina to binder design. Their contributions are orthogonal to ours, focusing on modeling protein-proted interactions and inference-time search for that application.

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3 LA- AA-PROOTINA
3.1 MOTIVATION: PARTIALLY LATENT REPRESENTATION ATOMISTIC PROTBIN DESIGN
While prior works have been able to successfully tackle high-quality protein backbone design, fully atomistic structure generation comes with additional challenges. The model needs to jointly reason over large-scale backbone structure, amino acid types, and side-chains, whose dimensionality depends on the amino acid-thi represents complex continuous-cateoore generative modeling problem.
How can we best build top of successful backbone generation frameworks (Watson al. 2023 Geffner et al., 2025 Lin et al. 2024), while addressing the additional fully atomistic modeling challenges? We propose to encode per-residue atomistic detail and residue type in a fixed-lengthe con- tinuous latent space. while maintaining explicit backbone modeling through the a-carbon coordinates. This has several key advantages: (i) By encoding atomistic details, including varying-lenght side chains, together with their categorical residue type, into fixed-length.Ji fully fullly-continuonn latent space, we elegantly avoid mixed continuous continuous-categorica modeling challenges in the model's main generative component. Together with the continuous backbone coordinates, the per-residue latent variables can generated using efficient, fully-continuous flow matching methods, while mixed modality modeling complexities carbon-based backbone representation in La-Proteina's hybrid, partially latent framework. That way, can build on top of advances in high-performance backbone modeling. Our ablations show that also encoding a-carbons in latent space leads to significantly worse results (ablations in App. G.1.3). (iii) Maintaining explicit backbone modeling capa- bilities also allows us to use different generation schedules for global a-carbon backbone structure and per-residue atomistic (latent) details (see Sec. (3.4). critical detail in our framework to achieve high performance (ablations in App. G.2). We argue that our hybrid approach is a key reason why La-Proteina significantly outperforms existing latent frameworks for protein structure generation, all of which opt for fully-latent modeling instead. (iv) Our partially latent framework increases scalability. Explicit modeling of all atoms in large proteins may require complex and memory-consuming neural networks- in fact, for that reason some approaches that treat all atoms explicitly can only be trained on small proteins (Qu et al.) (004)). In contast, La- Proteina's 's per-residue latent variables simply become additional channels top of the o-carbon coordinates, enabling the application of established, high-performant
handled by encoder and decoder. (ii) It is critical maintain the explicit
SIUS task
GEBR task
Figure 3: Atomistic Motif Scaffolding. La- Proteina accurately reconstructs the atomistic mo- tif (red), while generating diverse scaffolds. Vi- sualization overlays generated protein and motif.
architectures (Geffner et al. 2025) without increasing the length of internal sequence representations. Hence, manageable, and scale the model to large protein generation tasks of up to 800 residues (see Sec. 4.1)
keep the model's memory footprint
Next, introduce La-Proteina (Fig. D.. First, train VAE, with its encoder mapping input proteins (sequence and structure) to latent variables, and its decoder reconstructing complete proteins from the latent variables and c-carron coordinates. Leveraging the VAE, then train flow matching model to learn the joint distribution over latent variables and coordinates of the o-carbon atoms.
Notation. L denotes protein length, Xc, E RL3 the a-carbon coordinates, .C. E LL the coordinates of other heavy atoms (Atom37 representation without a-carbons, see Sec, 2 E (0, ..., 1 the protein sequence, and E _Lx8 the (8-dimensional) per-residue latent variables.
3.2 PROBABILISTIC FORMULATION
We learn a latent variable model p(xc, X .,, z), trained so that its marginal p dz approximates the target distribution over proteins Pdata (Xc., X 8). Central to our approach is the factorization
(x,,
&C,,8, z) XC, po(xc., ; 2) pol Cu. (c.,
(1)
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which enables the model to capture complex dependencies between backbone, sequence, and side chains through the latent variable z. The first component of this factorization, pe (xc... z), defined over continuous. per-residue, sxed-dimensional space, is captured by our partially latent flow matching model (Sec. (.2.2).. The second component, Pa (x . S| XC. 2), denotes the VAF's decoder, which, together the encoder, maps between latent variables and proteins and handles complexities arising from mixed discrete/continuous data types (sequence and structure), and the variable dimensionality of side chains. Critically, by conditioning on both a-carbon coordinates XC. and expressive latent vari- ables z, this conditional distribution can be effectively represented by simple factorized distributions.
3.2.1
VARIATIONAL. AUTORNCODER
The VAE's decoder models sequence and full- full-atom structure. Formally, it parameterizes the con- ditional likelihood term (x s conditional independence between the sequence s and the coordinates of non-a-carbon atoms x C.
XC.: 2) from Eq. ( We model this distribution assuming
Pp(x-C,, s| XC. 2) ( Xc. Po xC,,
(2)
where we define (s XC,, 2) as a factorized categorical distribution and p factorized Gaussian with unit variance. These choices are standard in the VAE literature (Kingma et al.) 2013), justified by expressive conditioning on the latent variables and q-carbon coordinates, which capture underlying dependencies and enable accurate approximations using simple factorized forms.
XC., Z) as
The decoder network takes the latent variables z and c-carbon coordinates XC. as input, producing parameters for the distributions over sequence and non-a-carbon atom coordinates x x-C.. To handle the varying con-a-carbon atom count across residue types while maintaining a fixed output dimension- ality, the decoder generates Atom37 coordinates for each residue structure, yielding a [4,37, 37,3] tensor. The appropriate subset of all Atom37 entries is selected on the basis of the sequence, using the ground truth sequence during training (supervising only the selected entries) and the decoded sequence during inference. Further, the coordinates of the a-carbons are set to the ones passed input.
The VAE encoder, on the other hand, is used to map proteins to their corresponding latent represen- tation. Formally, the encoder parameterizes qu (z XC., x , s), factorized Gaussian designed to approximate the posterior distribution Po.0(2 XC, X , This network takes the complete protein structure (XC.> X-C,, 8) as input, and outputs the mean and log-scale parameters for qo (z I-).
The encoder and decoder are optimized maximizing the 3-weighted ELBO (Higgins et al., 201 7).
common objective for VAE training in the context of generative modeling in latent spaces, given by
max Epasta (xc, xx-C, :))9 (x)...) (x)..) [log (x-c. s|xc.. z)] 3 KL (z)xc. X-C., s) s)z()) (3) 0.4
For the modeling choices described above, the reconstruction term in Eq. reduces to the cross entropy loss for the sequence and the squared Lg loss for the structure. For training, we set 3 = 10" and use standard isotropic Gaussian prior over latent variables p(z) =x 0,
3.2.2 PARTIALLY LATENT FLOW MATCHINN
The second stage of training La-Proteina involves optimizing a flow matching model to approximate the target distribution p (XC, z) This model trains a denoiser network Ve ve zz= 1z. 12.t% tx) to predict the velocity field transporting samples from standard Gaussian reference distribution, Po(xe: 22), to the target data distribution, pr (x(,, z )) for tæ t2 E [0, 1]. These are defined as
Po (x 2 = N (xf. 0, (2 1), and Pi (x.., x²) Pdata (Xc. z).
(4)
The denoiser network Vo trained by minimizing the conditional flow matching (CFM) objective
min E v (x'o ,==,tz,,t, (t,,tt)) (xc. x2. (x(C 2²= (t,t,,tz) (z (z- z²) [1]] (5)
where the expectation over ( 2) (i.e., pı), noise distributions Ax22, 10, I) and (222 0, I) (i.e., Po), and interpolation time distributions Pt, (tz) and Pt,, (tz). The use of two
For this stage the VAE parameters are frozen. The target distribution over a-carbon coordinates and latent variahles is defined by the data distribution Pastal (XC,, x .5).5) and the VAE encoder gs (z) XC.: x .C.. 5), and can be sampled by (xc.. X S) ~ Paata (xC,, , x- Ca 8) and ~ qo NC., x 8). P
5

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separate interpolation times tr and f2 is critical design decision that enables the of different integration schedules for the coordinates of the d-carbons xc, and latent variables z during inference. This flexibility is vital for achieving strong performance; employing a single, coupled time t would enforce an identical schedule for both modalities, which leads to worse results (see App. G.2
The specific form for the time sampling distributions represent an important design decision (Esser et al. 2024). Inspired by /efffnr et al. (2025), who, in the context of backbone design, employ a mixture of Uniform and Beta distributions, we adopt independent sampling for by and b9 given by
Pt. 0.02 (n, 1) 0.98 (eta(1.9,1) and Pt. = 0.02 Uni 1) + 0.98 Beta(1, 1.5), (6)
visualized in Fig. 13 The distribution parameters were chosen based our observation that generating backbones using a faster schedule than that used for the latent variables yields superior results during inference (see Sec. (.4). Hence, the distributions from Eq. 4 were chosen so that time pairs that satisfy l > 1z, relevant for the used inference schedules, are sampled more frequently.
3.3 NEURAL NETWORK ARCHITECTURES
The neural networks used by La-Proteina, the encoder, decoder, and denoiser, rely on a shared core architecture based on transformers with biased attention mechanisms (Jumper et al. 202I), with our implementation closely following Geffner et al. (2025). While built on this common foundation, the three networks are distinguished by their specific inputs, outputs, and conditioning mechanisms. For instance, the encoder takes as input full proteins and outputs per-residue latent variables, while the decoder produces full proteins given latent variables and a-carbon coordinates. Additionally, the denoiser is conditioned on interpolation times (1z, (2) using adaptive layer normalization and output scaling techniques (Peebles & Xie 2023). The encoder and decoder each consist of approximately 130M parameters, while the denoiser totals 160M. A key architectural choice for scalability is that our main models omit computationally expensive triangular update layers (Jumper et al. (021), ) which, while effective in structural biology tasks (Lin et al., 2024 Abramson et al. 20024). incur significant memory and compute costs. Following Geffinr et al. (2025), La-Proteina achieves high performance using only efficient transformer networks, maintaining strong scalability. These triangular multiplicative layers can optionally be added to improve pair representations and enhance protein co-designability (see Sec. 4.1 We include architectural details in App. H
3.4 MODEL SAMPLING
New proteins can be generated by La-Proteina by sampling latent variables and a-carbon coordinates using the partially latent flow matching model, and then feeding these through the decoder (Fig. D.
Sampling the partially latent flow matching model. As we use Gaussian flows (Sec. 2 we can esti- directly from vo (Albergo et al. 2023) (see App. E Access to scores enables the use stochastic samplers to generate pairs of c-carbon coordinates and latent variables (xc.. z). We generate such samples by simulating
mate the score of intermediate densities <(x²g_ z'', . tt,, t2) x V log p/= (x'g. z²
the following stochastic differential equations (SDEs) from (lz, (2) = (0, 0) to (tz, tx) = (1,
dx's. vv (x'e,, zt= tax to dtzz + (a. (xx(tt) z²t,t tz) + 228x aW, dz vv z²x tz, tx (xx) tt, dt, + v /28 (to) M: dW,.-
(7)
Here, 3g and B3 are scaling functions that modulate the contribution of the Langevin-like term in the SDEs (Karras et al. (022) (details in App. E). We also use noise scaling parameters 7) and 7). set to values less than or equal to one, to control the magnitude of the injected noise. This follows common practices in protein design; virtually all successful flow matching and diffusion-based methods adopt some form of reduced noise or temperature sampling, as has been consistently observed to improve
(co- (ee->ddeinnnblitt. albeit at the cost of reduced diversity (Yim et al. [023a] Watson et al. 2023 Lin
[ct al. 2024. Bose et al. 20244 Wang et al. 2024a Campbell et al. 2024| Geffner et al. 2025).
We use the Guler-Maruyama method (Higham) 2001 to simulate Eq. 7 As discussed, independently scheduling the generation of a-carbon coordinates XC. and latent variables z is critical for good performance. Our empirical findings indicate that discretization strategies that generate xc, at a faster rate than z yield improved results over alternative choices. Full details of our sampling algorithms, including ablations for these discretization schemes, are provided in Apps. F. and

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Table I: La-Proteina achieves state-of-the results on unconditional all-atom design, for lengths between 100 and 500 residues. Diversity, novelty, and secondary structure computed on all-atom co-designable samples. The tn suffix indicates La-Proteina with multiplicative triangular update layers to update the pair representation. The and n. denote the noise scaling factors during generation (Eq. (7). J. Best scores bold, second best underlined.
Method
Co-designailliy (9)
PLDDT
Diversity (A clusters)
Novelty
Designabilit (5) 1
Sec. Stz. (%)
All-atom
o-catbon
(St 2 80)
Str
Sog
S
PDB
AFDB
MPNN-8
MPNN-1
e
Ptall atom)
36.7
37.9
92
134
148
165
0.72
0.81
57.9
44.1
56
17
Proipandelle-Ie
62.0
14
12.2
85
64
0.89
61.8
PLAID
11.0
19.2
44
25
38
27
0.89
0.92
37.6
23.8
44
14
Proteinfeenerator
9.8
17.8
52
12
28
24
0.83
0.89
54.2
42.8
78
5
Protpantelle
8.8
35.2
37
10
37
21
0.79
01.2
56.2
43.8
65
14
Le Proteina (u.-1) (..1.0.1)
68.4
72.2
97
206
216
301
0.75
0.82
93.8
82.6
72
5
Proteine (n., qol 0:1)
97
197
Proteina (1u-%u) (0.3.0.1)
59.6
95
180
189
94.6
76.0
Le-Prtte Proteina en (A.. n2) (0.1. 0.13
75.0
78.2
100
129
199
247
0.82
0.86
94.6
84.6
73
6
La- ProPttiin on (a.: (o) 0..3..13
21.6
25.8
29
166
211
294
0.79
0.85
95.2
83.4
66
9
Sampling the VAE decoder. The a-carbon coordinates xC, and latent variables z produced by the flow matching model are passed to the VAE decoder. The non-a-carbon coordinates X-C, are then obtained by taking the mean of the Gaussian distribution (x(x c... XC.. 2), while the amino acid sequence is determined by taking the arg max of the logits of the categorical (s(s) XC.: 2).
4 EXPERIMENTS
We evaluate La-Proteine unconditional atomistic protein generation up to 800 residues well as on atomistic motif scaffolding, a critical protein design task. We train all models on a filtered version of the Foldseek cluster representatives of the AFDB (van Kempen et al. 2024), except for long protein generation where we train on a custom subset of the AFDB consisting of 4-6 samples. Unless otherwise specified, our trained La-Proteina models omit triangular update layers; any use
of such layers is explicitly noted (used for a single model in Sec. [4.1). Full experimental details, including datasets, metrics, and training procedures, well ablations, in Apps. [aadd G
4.1
UNCONDITIONAL PROTEIN STRUCTURE GENERATION BENCHMARK
Tab. D compares two variants of La- La-Protei,a, one with triangular multiplicative layers and one without, against publicly available all-atom generation baselines, including P(all-atom) (Qu et al. 2024), APM
(Chen et al. 2025), PLAID eLu al. 2024). ProteinGenerator (Lisanza et al. 2023), Protpardelle (Chu
et al. 2024) and Protpardelle-Ie Ic (Lu al. 2025 Each method was used generate 100 proteins for each length in (100, 200, 300, 400, 500 j. We assess performance using several metrics (described in App. D. including all-atom co-designability, pLDDT, diversity, novelty (against PDB and AFDB), and standard designability, the last being a metric typically used to evaluate backbone design methods. Co-designability evaluates how well co- co-generated sequences fold into generated structures, while designability uses ProteinMPNN (Dauparas et al. 2022) to produce sequences for generated structures. We note that our co-designability filter does not use a predicted local distance difference (pLDDTT cutoff; we instead report pLDDT values of successfully refolded samples separately.
Results in Tab. T show that both variants of L.-PPotei outperform all baselines in all-atom co-designability, designability, and diversity, while remaining highly competitive in novelty. Ad- ditionally, we observe that La-Proteina with triangular layers tends to achieve higher co-designability values, albeit at the cost of diversity, and that all La-Proteina models yield higher pLDDT values for successfully refolded samples than basclines (a more detailed PLDDT analysis is provided in Fig. 34). Crucially, La-Proteina without triangular multiplicative layers establishes sate-of-thhearn performance while being highly scalable. This contrasts sharply with the second- -bett performing method, P(all-atom). which relies on computationally expensive triangular update layers (Jumper et al. 2021). thereby limiting it to short proteins. Due to its favorable scalability and performance, all remaining experiments in the upcoming sections rely La-Proteina without triangular update layers.
Generation of Large All-Atomistic Structures. To demonstrate scalability, we trained another version of La- Proteiia on an AFDB dataset with <46M samples with length up 896 residues
2 Protpardelle- Ic trained conditionally for atomistic scaffolding. However, Lu et al. (2025) did not train all-atom unconditional model. We sampled the conditional model unconditionally for this evaluation.
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Figure 5: La-Proteina produces structures with higher structural validity than existing all-atom generation baselines. MolProbity metrics assessing structural quality: overall score, clash score, Ramachandran angle outliers, and covalent bond outliers (details in App. D). P(all-atom) limited to 500 residues; generating longer proteins is computationally prohibitive. requiring over 140GB of GPU memory to produce single sample.
(details in App. C.I We see in Fig. A that La-Proteina performs best in terms of (co- )designability and diversity for the task of backbone design (left two panels) as well as all-atom design (right two panels). Notably, La-Proteina outperforms the previous state-of-the-arl Proteina method (Geffner ct al. 2025) in backbone design tasks at all lengths, and far ahead in co-designability compared to other all-atoom generation methods, which fail to produce realistic samples of length 500 and above.
Biophysical Analysis of All-Atom Structure Validity. To examine the biophysical quality of generated structures, we evaluate our model and all-atom baselines using the MolProbity tool (Davis et al. 2007) to assess the structural validity in terms of bond angles, clashes and other physical quantities. Fig. 3lsows that La-Proteina produces more high quality structures, scoring significantly better than all baselines. The structures generated by Ia-Proteina are the most physically realistic ones, similar to real proteins.
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Most side chain torsion angles do not vary freely, but cluster due to steric repulsions into so-called rotamers (Haddad et al. 2019). As second validation to judge the coverage of conformational space, we visualize side-chain dihedral angle distributions and compare their rotamer populations to PDB and AFDB references, similar how rotamer libraries operate (Dunbrack Jr. 2002). La-Proteing models these distribution accurately, shown in Fig. 6 for the tryptophan X1 angle. La- Proteina's 's samples accurately recover all major rotameric states as well as their respective frequencies with respect to the reference PDB/AFDB. In contrast, baselines often deviate from these references, missing modes or populating unrealistic angular regions. Plots for all residues and angles in App. D.3.2
4.2 ATOMISTIC MOTIF SCAFFOLDING
Two advantages all-atom generative models are their ability to incorporate atomistic conditioning in- formation well designing new protein structures independent of backbone rotamer constraints. To this end, we trained La-P Pr-Prtteina on the challenging task of atomistic motif scaffolding, where given the atomic structure of predefined motif the model should generate protein structure that scaf-
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All-Atom Motif Scaffolding
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Figure 7: Atomistic motif scaffolding, 26 atomistic motif-scaaffldiig tasks (x-axis), comparing Protpardelle (limited to indexed), Protpardelle-Ic (limited all-atom indexed), La-Proteina (indexed) and La-Proteina (unindexed). La-Proteina solves between and of the 26 tasks, depending on the task type (all- (all-atom or tip-atom,, indexed or unindexed), vastly outperforms Protpardelle (which solves 4 out of 26 tasks), and also outperforms Protpardelle- Ic, achieving a larger number of unique successes in 21 out of the 26 tasks. "# segments" refers to the number of residue segments in the motif. Detailed evaluation criteria in App.
folds this motif accurately. We assessed performance under two distinct levels of input motif detail: all-atom, where the model is conditioned on the complete atomic structure of the motif residues (back- bone and side-chain), and tip-atom scaffolding, where we only prespecify important functional groups after the final rotatable bond and let the model decide the relative backbone and rotamer placement. For each of these two tasks we test both indexed version, where the sequence indices of the motif residues are provided, and an unindexed version, where the model must also infer these positions, re- sulting in four evaluation setups. Across all setups design is successful if is all-atom co-designable, has an c-carbon motifRMSD A, and an all-atom motifRMSD <2Å. Complete details in App. F
Fig. presents the results for 26 atomistic scaffolding tasks, grouped by the number of continuous residue segments forming the motif. Our model consistently outperforms both Protpardelle-Ic, Ic, which is limited to indexed all-atom scaffolding, and its predecessor Protpardelle, which is restricted to indexed scaffolding. La-Proteina successfully solves most benchmark tasks across all four regimes: all-atom and tip-atom, for both the indexed and unindexed setups. Interestingly, for motifs comprised of three or more distinct residue segments, the unindexed version of La-Proteina consistently outper- forms its indexed counterpart. We hypothesize this is because fixing the positions of multiple segments limits the model's 's flexibility explore diverse structural solutions; the freedom determine the place- ment of the motif's residues in the unindexed setup is crucial for discovering a wider range of scaffolds. similar effect was observed by concurrent work (Faltings et al., 2025 Ahern al.) (025). Example scaffolds illustrating La- Proteina's is diverse and successful designs are shown in Fig. with additional
examples for tip-atom motif scaffolding of relevant enzyme active sites in Figs. 10 to 12 The results presented here evaluate La-P Pr-Prote structures directly; an alternative, more stringent evaluation using refolded structures (obtained by folding the produeeroddued sequences) is provided in Fig. 33. where it can be observed that La-Proteina achieves state-oftuee the-art performance under this evaluation well.
4.3 AUTOENCODER EVALUATION AND LATENT SPACE ANALYSIS
We assessed the VAE's reconstruction perfor- mance on a held-out test set, where it achieved a mean all-atom RMSD s0. 12Á and a perfect se- quence recovery rate of 1. Beyond reconstruc- tion, we analyzed the properties of the latent space. t-SNE visualization of the latent vari- ables (Fig g left) reveals distinct clusters corre- sponding to different amino acid residue types, indicating that latent variables effectively cap- ture residue-specifts features. In addition, we see that structurally (GLN/GLU, ASN/ASP) as well as chemically similar amino acids (aromatics like PHE/TYR/TRP) cluster together, indicating the latent space captures biophysically relevant features.
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Figure 8: Analyzing La-Proteina'ss 's latent space. t-SNE plot (left) and perturbation- based locality analysis (right).
To further probe the learned representation, we conducted a simple perturbation experiment: after en- coding protein, the latent variables associated with a single residue were perturbed with varying mag-

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nitudes. We observe that such localized perturbations single residue's latent vector predominantly impact the reconstruction of that specific residue, leaving other residues almost unaffected (Fig. g right; red: sequence reconstruction loss, blue: structure reconstruction loss). This "local behavior" of the latent representation is noteworthy: Although both the encoder and decoder use transformer archi- tectures capable of modeling long-range dependencies and jointly process the entire protein and all latent variables, our analysis suggests that each per-residue latent variable primarily encapsulates in- formation pertinent to its own corresponding residue, rather than distributing information non-locally.
5 CONCLUSIONS
We presented La- La-Proteina, a scalable and efficient all-atom protein structure generative model that achieves state-of-the-art performance in unconditional and conditional atomistic protein design tasks and can generate realistic atomistic structures of up to 800 residues. Our key design choice involves a partially latent flow matching model that inherits the performance benefits of backbone generative models while benefiting from per-residue fixed-size latent representation for sequence and side-chains, side-stepping scalability and accuracy issues that other methods suffer from. We believe that rofPrnn and its strong performance on atomistic design tasks, like unindexed atomistic motif scaffolding, could enable new important protein design applications, like binder and enzyme design.
6 ETHICS STATEMENT
The advancement of generative models for de novo protein design, including approaches like La- Proteina, offers the potential for significant positive impact across many scientific and societal domains. These technologies can significantly accelerate the discovery and development of protein- based therapeutics. In biotechnology and industry, computationally designed enzymes could pave the way, for instance, to greener chemical processes and sustainable materials. Alongside these benefits, new and improved tools for de novo protein design carry certain risks. While models in this area are developed for beneficial applications, any technology capable of designing novel functional proteins could, in principle, be misused if ethical oversight is not in place. This includes, for instance, the hypothetical design of proteins that could pose biosecurity threats.
7 REPRODUCIBILITY STATEMENT
To ensure reproducibility, we release code for La-Proteina at https:: https:://qithub gighubtthhugg.g com/ NVIDTA-Digital-Bin bitttta---iiolll--teeeeesee We also provide comprehensive experimental details in the Supplementary Material. This includes includes the precise filters used for dataset construction (App. model architectures (App. HD. and training parameters like GPU count and training steps (App. for unconditional generation, App. F. for atomistic motif scaffolding). We also include precise deseriptions and the exact commands used to compute all reported metrics (App.D]for metrics used to evaluate unconditional models, App. F3 for atomistic motif scaffolding).
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Jason Yim, Andrew Campbell, Andrew Y. K. Foong, Michael Gastegger, José Jiménez-Luna, Sarah Lewis, Victor Garcia Satorras, Bastiaan S. Veeling, Regina Barzilay, Tommi Jaakkola, and Frank Noé. Fast protein backbone generation with se(3) flow matching. arXiv preprint arXiv:2310.05297. 2023a.
Jason Yim, Brian L. Trippe, Valentin De Bortoli, Emile Mathieu, Arnaud Doucet, Regina Barzilay, and Tommi Jaakkola. SE(3) diffusion model with application to protein backbone generation. In Proceedings of the 40th International Conference on Machine Learning (ICML), 2023b.
Jason Yim, Andrew Campbell, Emile Mathieu, Andrew Y. K. Foong, Michael Gastegger, Jose Jimenez-Luna, Sarah Lewis, Victor Garcia Satorras, Bastiaan S. Veeling, Frank Noe, Regina Barzilay, and Tommi Jaakkola. Improved motif-scaffolding with SE(3) flow matching. Transactions on Machine Learning Research, 2024.
Jason Yim, Marouane Jaakik, Ge Liu, Jacob Gershon, Karsten Kreis, David Baker, Regina Barzilay, and Tommi Jaakkola. Hierarchical protein backbone generation with latent and structure diffusion. arXiv preprint arXiv:2504.0937. 2025.
Yang Zhang and Jeffrey Skolnick. Scoring function for automated assessment of protein structure template quality. Proteins: Structure, Function, and Bioinformatics, 57(4):702-710, 2004.
Qinqing Zheng, Matt Le, Neta Shaul, Yaron Lipman, Aditya Grover, and Ricky TQ Chen. Guided flows for generative modeling and decision making. arXiv preprint arXiv:2311.13443 2023.
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Appendix
Limitations and Future Work
17
Additional Visualizations
B.
Unconditional La- Proteina Samples
B.2 2
Atomistic Motif Scaffolding La-Proteina Samples
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C
nconditional Generation
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Datasets
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Training Details
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C.2.1 VAE training
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C.2.2 Flow Matching Training
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Baseline Sampling
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D Evaluation Metrics
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D.1
Co-Designability. Designability, Diversity, Novelty
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MolProhity for Structural Quality Assesment
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D.3 Side Odde-hhinn Dihedral Angle Distributions/
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D.3.1
Background amino acid rotamers
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D.3.2 Analysis of generated amino acid rotamers
27
E
Sampling
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Numerical Discretization Scheme
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F
Atomistic Motif Scaffolding
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FI
Training
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F2
Sampling
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F3
Evaluation
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F4
Evaluation via Retolded Structures
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Baseline Sampling
G
Ablations
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G.
VAE Ablations
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G.I.1
KL KL Penalty Weight
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G.1.2
Decoder Architecture
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G.1.3
Encoding a-carbons
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G.I.4
Results
G.2
Flow Matching Sampling Hyperparameters
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G.3
Main Conclusions from Ablation Studies]
39
H
Architectures
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Model Parameters, Sampling Speed and Memory Consumption
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Additional Results
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J.1
Novelty Results with Newer Foldseek Version
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J.2
Unconditional Evaluation on Shorter Proteins
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J.3
PLDDT Values
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J.4
Residue Type Distribution
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Declaration of Large Language Models Usage in this Work
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A LIMITATIONS AND FUTURE WORK
This work focuses on the de novo design of monomeric proteins using La-Proteina. While this scope allows for thorough investigation and demonstration of our partially latent approach for single-chain structures, we did not apply La-Proteina to the area of protein complex design. In biological systems, proteins typically function as components of larger assemblies. Handling protein complexes is critical for important tasks such as de novo binder design and enzyme design, which inherently require the modeling of full protein complexes and their interfaces. The instantiation of La-Proteina presented in this work was not trained to handle protein complexes. Our focus on monomers should be viewed as limitation of the current application scope rather than a constraint of the underlying La-Proteina framework. We anticipate that the principles of combining explicit structural modeling with latent representations could be fruitfully extended in future work to address the challenges designing functional protein complexes.
B ADDITIONAL. VISUALIZATIONS
B.1
UNCONDITIONAL La-Proteina SAMPLES
In Fig- 9 we show additional unconditional La-Proteina samples. Our model can generate diverse and co-designable fully atomistic proteins across broad range of sizes (residue count).
B.2 ATOMISTIC MOTIF SCAFFOLDING La-Proteina SAMPLES
we show additional atomistic motif scaffolding visualizations. All three figures show partial side chain scaffolding setups, where only the tips the conditioning side chains are given. The examples correspond to the scaffolding of enzyme active sites. We observe that the red conditioning motifs are exactly reproduced in almost all cases, and overall valid proteins are generated. Moreover, Fig. 12 demonstrates how La-Proteina can scaffold the same atomistic motif in diverse ways.
In Figs. to 12
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Figure 9: Fully atomistic unconditional La-Proteina samples. Numbers denote residue count. All samples co-designable.
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(a)
(b)
Figure 10: Atomistic Motif Scaffolding. Task IQIG (Delta(5)-3- Keetostrrd isomerase). The active site consists of an ASP that acts as general base, TYR stabilises the oxyanion another ASP that also stabilises the transition state by forming a hydrogen bond with the oxyanion. La-Proteina successfully generates a valid atomistic scaffold and accurately reproduces the red conditioning atoms that form the tip of partially given side chains (see zoom-ins moom-ins& (a)-c)). Side chains that involve conditioning atoms visualized as thick sticks, other side chains shown as thin sticks, Visualization overlays generated protein and atomistic motif.
transition state and
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(b)
(a)
(d)
(c)
Figure 11: Atomistic Motif Scaffolding. Task 5YUT (carbonic anhydrase). The active site here combines metal coordination site (HIS residues) with a hydrophobic substrate channel (VAL and TRP residues). La- Proteina successfully generates valid atomistic scaffold and accurately reproduces the red conditioning atoms that form tip of partially given chains (see zoom-ins (b)-(d). small inconsistency can be observed (a), where model generates an incorreetly rotated ring (we found such inconsistencies to extremely rarc). Side chains that involve conditioning atoms are visualized as thick sticks, all other side chains are shown as thin sticks. Visualization overlays generated protein and atomistic motif.
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(a)
(b)
(c)
(d)
(e)
Atomistic Motif
Figure 12: Atomistic Motif Scaffolding. Task SAOU (retro-aldolase). La- La-Proteina successfully generates diverse valid atomistic scaffolds and accurately reproduces the conditioning atoms form the tip of partially given side chains (see zoom-ins (a)-(d)). The atomistic motif is shown in (c) consisting a catalytic tetrad that emerged during directed evolution in the laboratory Obexer et al. (2017). with the LYS acting as catalytic nucleophile, the two TYR stabilizing the transtion state and participating proton transfer and the ASN maintaining the bydrogen-bond network that connects and spatially arranges all tetrad residues. We that Proteina can produce diverse solutions the scaffolding task (shown the four quadrants of the figure; note that each protein is visualized from different angles for best views of the active site). For clarity, we are only showing side chains of residues that involve conditioning atoms; all other side chains are generated, too, but not shown. Visualization overlays generated protein and atomistic motif.
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C UNCONDITIONAL GENERATION
C.I DATASETS
We use two datasets to train our unconditional models, one based on the cluster representatives of the Foldseek (van Kempen et al., 2024) clustered version of the AFBD, and another one based custom subset of the AFDB (for our long chain evaluation).
Foldseek Clustered AFDB. This dataset, previously used by Lin et al. (2024); Geffner et al. (2025)
is a filtered and clustered rendition of the AlphaFold Database (AHDB) (Barrio-Hernandee Hernandez et al. 2023). The clustering employs both sequence (via MMseqs2 (Steinegger & Söding, 2017)) and
structure (via Foldseek (van Kempen et al. (2244) information. The resulting dataset is composed of cluster representatives, meaning one structure selected from each cluster. This initially yields approximately three million unique samples. We further refine this set based on several criteria: minimum average pLDDT score of 80, protein lengths constrained to the 32-512 residue range, and specific secondary structure characteristies. For the latter, samples are retained only if their coil proportion below 50% and they contain no more than 20 consecutive coil residues (these coil filters are variants of those proposed by Qu et al. (2024). Critically, we also enforce the presence of beta sheets in the selected samples. This beta sheet filter was introduced because models trained without it, despite achieving state-of-thes of-thh-art metrics, generated proteins with a low beta-shect content (around 3-4%).. Incorporating this filter corrects this imbalance, leading to models that produce samples with an average beta-sheet content of approximately 10%. These cumulative filtering steps result in final curated dataset of approximately 350k protein samples.
Custom AFDB subset for long length training. To create dataset that is focused on longer samples, we created a custom dataset starting from the AlphaFold database. We filtered for a minimum average PLDDT of 70 and length between 384 and 896, resulting in 46,942,694 structures. For training we then cluster with MMSeqs2 at a sequence similarity of 50% and sample then randomly from the resulting 4,035,594 clusters at training time.
C.2 TRAINING DETAILS
C.2.1 VAE TRAINING
The details of the VAE encoder and decoder architecture are given in App. H Briefly, both networks consist of 12 transformer layers, totaling approximately 130M parameters. These architectures trained jointly maximizing the Evidence Lower Bound from Eq. (3). We optimize using AdamW (Loshchllvv Hutter 2017) with a learning rate of 0.0001 and a weight decay factor of 0.01. We also use exponential moving average with a decay of 0.999. VAEs are trained on the Foldseek clustered AFDB (without including the filter for the beta sheet content). We train in multiple stages: (i) Filtering for proteins between 32 and 256 residues, for 500k steps, on 16 NVIDIA A100-80GB GPUs; (ii) Filtering for proteins between 32 and 512 residues, for 140k steps, on 32 NVIDIA A A100-80GB GPUs; (iii) Filtering for proteins between 32 and 896 residues, for 1 180k steps, on 32 NVIDIA A100-80GB GPUs. We use the VAE parameters obtained after stage (ii) to train flow matching models limited up to 512 residues, and use the VAE obtained after step (iii) to train our flow matching model for longer proteins, up to 800 residues. For all models we use exponential moving average with a decay factor of 0.999.
C.2.2 FLOW MATCHING TRAINING
The details of the denoiser network architecture are given in App. H Briefly, consists of 14 transformer layers, totaling approximately 160M parameters. We train three models for unconditional generation, minimizing the conditional flow matching loss from Eq. (5). First, one without triangular multiplicative update layers, on the Foldseek Clustered AFDB dataset limited to 512 residues. We train this model for 390k steps, using Adam (Kingmal 20144) with learning of 0.0001, on 48 NVIDIA A100-80GB GPUs Second, a model with triangular multiplicative update layers, the Foldseek Clustered AFDB dataset limited to 512 residues. We train this model for 120k steps, using Adam with learning rate of 0.0001, multiplicative update layers for proteins of longer lengths, trained on our custom AFDB subset for long length proteins up to 896 residues (App. C.1). We train this model for 140k steps, using Adam
96 NVIDIA A100-80GB GPUs. Third, model without triangular
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with learning rate of 0.0001, 128 NVIDIA A100-80GB GPUs. For all models exponential moving average with a decay factor 0.999.
As discussed in Sec. 3.2.2 the interpolation times for a-carbon coordinates, tg. and for latent variables, fz, are sampled independently using the distributions from Eq. (6). This distributions are visualized in Fig.
Pu-mo 02 unif 0.98-pp1.3,
$11.9, 111
Pr myxmmooo.00 unit ArL o, 1,50
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Figure 13: La- ca-Proteina sampling distributions for interpolation times tu and tz..
C.3
BASELINE SAMPLING
Our main evaluation compares La-Proteina against publicly available models for all-atom generation, including P(all-atom) (Qu et al. 2024), PLAID (Lu et al.] 2024). Protpardelle (Chu et al. 2024). ProteinGenertor (Lisanza et al. (023), and APM Chen al. (2025). For each baseline we produce 100 samples for each protein length in { {100, 200, 300, 400, 500, 600, 700, 800} (for a total of 800 samples per model) using the official implementation from the corresponding Github repository.
P(all-atom). We use the code and weights as described in the original implementation F This model relies triangular attention layers (Jumper al., (02T). which have cubic memory and computational complexity. This limits the length of the proteins that P(all-atom) can generate. Using GPU with 140GB of RAM, were unable generate samples beyond 500 residues, due running out of memory. (This is for generating single sample.)
Protpardelle. We follow the instructions in the original repository using the al allatom_state_iie tth checkpoint
Protpardelle-Ic. This model is Protpardelle's successor, with focus conditional generation (atomistic motif scaffolding and protein complexes). We follow the instructions in the original repository using the cc91_epoch383 model We note that this model was trained conditionally for atomistic motif scaffolding, which takes an atomistic motif as input (conditioning information). However, Lu al. (2025) did not train an all-atom unconditional model. We therefore sample the conditional model unconditionally, simply done by not providing an atomistic motif as conditioning input.
PLAID. We use the 100M parameter model, as described in the original implementation! X The lengths of proteins sampled with PLAID are {96, 200, 296, 400, 496, 600, 696, 800), since the model only supports sampling proteins whose length is divisible by eight.
ProteinGenerator. We follow the instructions in the original implementation using the base checkpoing nt Uusig 100 steps to generate each sample since this is the recommended setting for higher quality, especially at longer lengths.
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APM. We follow the instructions for unconditoinal generation in the original implementation, using the default values for all parameters R
Fig. in the main paper reports metrics for the backbone design task, in which the sequence and
all-atoms except the a-carbons are ignored. For this specific set of results, we also compare against
several backbone design methods, including Chroma (Ingraham et al. 2023). Proteina (Geffner
iet al. 2025), Proteus (Wang et al. (024a)) Genie2 (Lin et al. 2024), FoldFlow (Bose et al. (024)).
RFDiffusion (Watson al. 2023 FrameFlow (Yim et al., 2023a). Frameeiff' (Yim et al.) 2023b).
and ESM3 (Hayes et al. 2024). For these models, we got the results from Gettiner et al. (2025).
making sure we use exactly the same metries reported in that work, to enable direct comparisons.
D EVALUATION METRICS
D.1 CO-DESIGNABILITY DESIGNABILITY, DIVERSITY, NOVELTY
Co-designability. The co-designability metric captures the degree to which between the sequence- structure pairs produced by a model aligned, by analyzing whether the produced sequence folds into the corresponding structure. This is done by measuring the all-atom RMSD between the structure produced by the model and the structure obtained using ESMFold (Lin et al. 2023 fold the corresponding sequence. If this all-atom RMSD is less than 2 the sample is deemed all-atom co-designable. The metric reported is the percentage of co-designable samples produced by model.
Designability. Designability, on the other hand, aims capture whether there is a sequence that folds into the produces structure (it ignores the produced sequence). This metric is typically used to evaluate backbone design models, which do not produce sequences. Given the produced structure. ProteinMPNN (Dauparas et al., 2022) is used to generate set of M sequences (using a sampling temperature of 0.1), ESMFold (L.nn al. 2023) used to fold all sequences, and finally the a-carbon RMSD between the original structure and each of the ESMFold produced structures is measured. A sample is deemed designable if the minimum of these M RMSD values is less than 2Å. We report two variants of this metric, using M=1 and M=8, denoted as MPNN-1 and MPNN-8 in Tab. 11
PLDDT. The Predicted Local Distance Difference Test (pLDDT) is per-residue confidence score, scaled from () to 100, that estimates the local structural accuracy of a predicted protein model (in our case ESMFold). Generally, the threshold of pLDDT 2 80 used to indicate high confidence and reliable predictions. The metric for the full protein is obtained by averaging these per-residue scores across the entire structure, averaged over succesfully refolded samples (i.e., all-atom co-designable samples).
Diversity. All three diversity metrics ("Str", "Seq", "Str+Seq") reported in Tab. T are obtained by clustering the subset of all-atom co-designable samples produced by model and reporting the number of clusters obtained. The difference between these metries is the clustering criteria used. Briefly, "Str" measures the diversity in the produced structures (ignoring sequence), "Seq" measures the diversity in the produced sequences (ignoring structures), and "Str+Seqq measures the diversity taking into account both the sequence and structure of the samples produced.
Structure diversity ("Str"). We cluster using the Foldseek command
foldseek easy-cluster spath_samplest <path_ <path_tmp>
cov mode 0
--aaiggneette inpiggmentttype 1
--min-seq-id 0
1 0.5
where <path_samples> is the path to a directory containing all-atom co-designable samples, gppathreesuttee is the directory where results will be stored, and path path_tmp is the directory used to store temporary files used by the clustering algorithm. This command clusters all produced structures without taking the corresponding sequences into account.
Joint structure and sequence ("Str+Seq"). We cluster using the Foldseck command
"https://gi wtt.:ttt.......eeeeeeeeeee www..////yttaane/aaa.....
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foldseek easy-cluster <path_samples> Opath_resulte <path_tmp>
-cov-mode 0
-~aligneettttype 2
--min-seq-id 0.1
- 0.5
Sequence diversity ("Seq"), We cluster using the MMSeqs2 command
mmseqs easy-linclue
pestt_input___ fi fi filepath> pdb_cluster <path_tmp>
--min-seq--ie 0.1
0.7
-- --oo-mode 1
where <fasta input_niilepaaeeeeeteeeeeeeeeeee filepath> is the path for the fasta file containing the sequences for all-atom co-designable samples.
Novelty. This metric assesses the structural similarity between samples generated by model and a defined reference set, where lower scores signify greater novelty (i.e., less resemblance to known structures). To calculate this, we compute the TM-Score Zhang & Skolnick (2004) between each all-atom co-designable sample generated by the model and every protein within the specified reference set. For each generated sample, its maximum T'--Score, reflecting its similarity to the closest structure in the reference set, is identified. The average of these maximum scores across every all-atom co-designable samples then reported as the novelty value. Given that TM-Scores range from 0 to 1, with higher scores indicating higher similarities, lower novelty scores are preferable. Tab. I presents novelty values against two reference sets: the PDB, as provided by Foldseek van Kempen et al. (2024) (labeled "PDB" in the table), and filtered version of the Foldseek Clustered AFDB, detailed App. C.T (minimum average pLDDT of 80, lengths 32-512 residues; labeled "AFDB" in the table). We use Foldseek (van Kempen et al., 2024) to compute TM-Scores of the produced samples against the corresponding reference set. The Fodlseck command used to compute this metric is given by
foldseek easy-search seath_sample> <reference laaerrence_ddttbbae___eeee <path_ reathtsee <tmp_path>
--a -aligneen-tyype 1 exhaustive-search
tmscore-tthreshold 0.0
-max-seqs 10000000000
-- -format-outpur query, a
where <path_sample> is the path for the PDB file containing the generated structure, and is the path of the dabaset used as reference.
cxefereene__dttbbsee_pp
Note Foldseck version used for novelty computation. Tab. I reports Novelty results using Foldseck version 9.427df8a. We note that newer Foldseck versions return different values for the exact same command and samples. Tab. shows Novelty results for all methods using Foldseck version c0.94 The table only reports Novelty values, as all other metrics are exactly the same as in Tab. 1
D.2 MOLPROBITY FOR STRUCTURAL QUALITY ASSESMENT
MolProbity (Davis et al., 2007) is widely used software designed for comprehensive validation of 3D macromolecular structures, primarily proteins and nucleic acids. assesses the quality of structure by analyzing its geometry, stereochemistry, and interatomic contacts against well-established chemical and physical principles derived from high-resolution experimental data. Its goal is to identify problematic regions in structure that may indicate errors or physically unrealistic conformations.
For our comparative analysis of generated protein structures, we focused on the following key metrics reported MolProbity:
MolProbity Score (MP score): This composite score that combines multiple individual geometric assessments (including clash score, Ramachandran favorability, and side-chain rotamer quality) into a single, log-weighted metric. It provides an overall indication of structural quality. Lower MP scores better; scores around 1.0-2.0 generally indicative of well-resolved and accurate experimental
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Figure 14: Additional MolProbity metrics. Rotamer outliers and Ramachandran outliers. While most baselines degrade especially at longer lengths, La-Proteina and P(all-atom) have realistic scores for all lengths. P(all-atom) evaluation only goes up to 500 residues due to memory limitations, for longer samples more than 140GB of GPU memory are needed to produce single sample. P(all-atom) and La- La-Proteina lincs mostly overlap until length 500 when the P(all-atom) line stops.
structures, while scores significantly above 2.5-3.0 often suggest increasing numbers of geometric and stereochemical issues.
Clash Score: This metric quantifies the severity of steric clashes by reporting the number of unfavorable all-atom overlaps (where van der Waals shells interpenetrate by 2 0.4A) per 1000 atoms. absolute cutoff, high-resolution X-ray crystal structures typically have clash scores below 20, often much lower (e.g.. <10). NMR structures lower-resolution crystal structures may exhibit higher values (e.g.. up to 50-60 or more could still be acceptable depending on context), but excessively high scores indicate significant packing problems.
A lower clash score signifies more sterically reasonable structure. While there's
Ramachandran Angle Outliers: This evaluates the conformational plausibility of the protein backbone by analyzing the Ramachandran plot, which describes allowed regions for the phi (ω) and psi (1) dihedral angles of amino acid residues. The metric reports the percentage of residues whose (ò, v) angles fall into disallowed (outlier) regions. For high-quality structures, this value is expected to be very low, ideally less than 0.2%, with modern well-refined structures often achieving <0.1 % outliers.
Covalent Bond Geometry Outliers (Bond Lengths and Angles): This metric assesses the cor- rectness of covalent geometry by comparing observed bond lengths and bond angles to standard dictionary values. It typically reports the percentage of bonds angles that deviate significantly (e.g., by more than standard deviations, or other thresholds defined by MolProbity) from these ideal values. A low percentage of outliers (ideally <1% % for both lengths and angles combined, or individually) indicates good covalent geometry.
Rotamer Outliers: This metric evaluates the plausibility of side-chain conformations by comparing the observed (chi) torsion angles of amino acid residues to distributions derived from high- high-quality experimental structures. MolProbity
comprehensive, data-driven rotamer library (the "ultimate" rotamer library) constructed from a large set of rigorously filtered protein chains to define statistically favored, allowed, and outlier regions for side-chain dihedral angles. A residue is classified rotamer outlier if its side-chain conformation falls into region sampled by less than 0.3% of reference structures, indicating a highly unusual energetically unfavorable state. High-quality protein structures typically exhibit less than 1% rotamer outliers, with modern structure determination and refinement methods often achieving even lower values. Elevated levels of rotamer outliers may suggest errors in side-chain modeling, poor electron density, physically unrealistic conformations, and thus serve as a sensitive indicator of local model quality.
Together, these MolProbity metrics offer a robust and multi-faceted evaluation of the atomistic accuracy and realism of the generated protein structures. MP score, clash score, bond length outliers and bond angle outliers are visulized in Fig. while ramachandran angle outliers and rotamer outliers are depicted in Fig. [4] In all of these we see that La- Proteina generates highly realistic structures at all lengths, whereas all other baselines generate less plausible structures and especially degrade at longer lengths (the exception is P(all-atom) that also has bad scores for clashes, angle outliers and bond outliers but scores well for rotamer outliers and Ramachandran outliers).
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D.3 SIDE-CHAIE DIHEDRAL ANGLE DISTRIBUTIONS
D.3.1 BACKGROUND ON AMINO ACID ROTAMERS
When investigating side-chain conformations in protein structures, one quickly recognizes that these side-chain torsion angles (denoted by XI, X2, etc., down the side chain) do not appear randomly and do not usually occur in broader regions such as backbone torsion angles which are usually visualized in Ramachandran plots Carugo & Djjnovié-Caruge that are called rotamers, i.c., chemical species that differ from one another mostly due to rotations about one or more single bonds Dunbrack Jr (2002).
(2013). but cluster into distinct conformations
This discreteness of the side-chain degrees-of soarces-oo-frredoon freedom is caused by steric repulsion between atoms three bonds away from each other, at the end of the atoms making up the plane of the torsion angle under question. To not cause too much steric repulsion, these groups usually prefer to adopt staggered conformations in which they are 60 degrees off-set the next group instead of eclipsed conformations where they overlap with this next group Clayden et al. 2012). The three possible staggered conformations (gauche plus at 60 degrees, gauche minus at -60 degrees and trans 180 degrees between the two groups under question) are the major rotamers that are visible in most X1 and several X2 plots Lovell et al. (2000). For example, in the case of X1, the plane of this torsion angle is formed by the CA and CB atom and the atoms under question for staggering are the N and for example the CGI in the case of VAL and ILE or the OG in the case of SER. Due to this, the angle XI is always rotameric at +60, 180 and -60/300 degrees (i.e. it falls into discrete angles), except for alanine which only has a hydrogen instead of CG and therefore no X1 rotamer and glycine which has neither CB nor CG.
However, the populations of these rotamers are different based on amino acid identity. Usually the preference declines in the order of g- (-60), trans (180), and g + (60), but there are exceptions. PRO for example has a tight ring structure that only allows for two X1 rotamers at around -30 and +30 degrees (Fig. 2 SER and THR on the other hand prefer the g+ (60) rotamer since in that conformation it can form a hydrogen bond to the backbone with their oxygen atom. ILE, LEU, and THR have two gamma heavy atoms, which cause one rotamer always be in an unfavorable conformation; these amino acids only show two X1 rotamers with significant populations.
There are also non-rotamerie degrees of freedom. While in ARG for example both xi and X2 are rotamer (Fig. [5). leading to 9 configurations. ASP for example has non-rotameric X2 angle that spreads over rather continuous spectrum (Fig. [7]. These non-rotameric degres of freedom are always the last one in the side chain, i.e. the furthest away from the backbone. In the case of ASN and ASP this X2 (Fig. [6 and Fig. [7]. whereas in the case of GLN and GLU this is X3 (Fig. 19 and Fig. 20 first row). Beyond this, there are further factors determining rotamer populations, either wreckbone-indppendeee bockbone-dependen ones Chakrabarti & Pal (2001).
effects like syn-pentane interactions Dunbrack Jr Karplus (1994) or
D.3.2 ANALYSIS OF GENERATED AMINO ACID ROTAMERS
To not only look at outright rotamer outliers, but also rotamer frequencies and mode coverage, we visualize Kernel Density Estimation (KDE) plots for all side chain angles of all amino acids in Figs. 15 to 31 We conduct this analysis for the samples generated for La- Proorrteena, all baselines, and two reference datasets from the PDB and AFDB (100 structures for each length of 100 to 800 in steps of 100). The PDB data set was curated by selecting 100 X-ray structures with a resolution below 2 of the respective length +5 residues (for length 800, which leads to 60 structures). The AFDB reference data set was curated similarly, just with the filtering threshold being a pLDDT score above 80 and a radius of gyration of less than 3 to avoid overrepresentation of side-chain angles corresponding to extended alpha-helices.
As in the main text, we see that La-Proteina often captures not only the correct modes, but often also at approximately the correct rotamer frequencies with respect to the reference datasets from the PDB and AFDB. This can be seen, for instance, for ARG X3 (Fig. 15 HIS X2 (Fig. 21) or PRO X1 (Fig. 27). D. P(all-atom) and Protpardelle often miss modes completely, while PLAID and ProteinGenerator often get the modes correctly but represent them in different frequencies compared to the base dataset. We also see that for some side-chain angles, the distribution between PDB and
AFDB differ significantly, as for ARG X4 (Fig. 15). LYS Xa (Fig. 24 and LYS X4 (Fig. 24 sixth row
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left). In these cases, La-Proteina adheres more closely the AFDB reference since it trained on AFDB structures; however, interestingly none of the other methods capture the PDB modes here as well despite being trained on datasets including the PDB.
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Figure 15: Side-chain angles for amino acid ARG.
Figure 16: Side-chain angles for amino acid ASN.
Ade
Auly
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Figure 17: Side-chain angles for amino acid ASP.
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Figure 18: Side-chain angles for amino acid CYS.
2.4
Valande
A44
0850
Figure 19: Side-chain angles for amino acid GLN.
3.5
4.4
Figure 20: Side-chain angles for amino acid GLUU
3:21
0.0
Figure 21: Side-chain angles for amino acid HIS.
Figure 22: Side-chain angles for amino acid ILEE.
0.50
Nallow
Z4cu
$10
Figure 23: Side-chain angles for amino acid LEU,
500
0.30
441
Tscm
0.2
Figure 24: Side-chain angles for amino acid LYS.
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0.0
Figure 25: Side-chain angles for amino acid MET.
041.5
Nelanee
fccm
0005
8400
300
Figure 26: Side-chain angles for amino acid PHE.
Figure 27: Side-chain angles for amino acid PRO.
44100
6455
0000
Figure 28: Side-chain angles for amino acid SER.
MEEE
Figure 29: Side-chain angles for amino acid THR.
B45
Figure 30: Side-chain angles for amino acid TYR.
020
Figure 31: Side-chain angles for amino acid VAL.
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E SAMPLING
We sample La-Proteina by numerically simulating the SDE from Eq. 7 This SDE relies on the score function (gradient of log probability) of intermediate densities. Since we use Gaussian flow and linear interpolants, we can compute these directly from the learned vector field Dy as (Ma et al.
2024
Zheng et al. 2023
t VV
zz (21,tt)t))
xCa
(" 2t to tx)
logPo(X's, x' (x:tz) tx)
(8)
1 tx
(*xx(,, 2 tx Lv 2/= 12,122)) 2/=
V zt log pa (x 2 t2)))).
Simulating the SDE from Eq. requires selecting the noise scaling parameters The and 7/s and the scaling functions (tx) and 32 (ty). which modulate the Langevin- like term in the SDE. For the former, we experiment with values [0. 1]. noting that 7),- 7)= = yields "unbiased sampling" (for any choice of 3r and 3_ (Karras et al. 2022)), and smaller values sample distributions which differ from the original one defined by the flow matching model (often referred to as "low temperature sampling" (Geffner al. 2025 Ingraham al. 2023 For the scaling functions use
and (12) = т
(1 1.))
tan
(10)
fr
2
2
We show ablations for these choices in App. G
E.1 NUMERICAL DISCRETIZATION SCHEME
We simulate the system of stochastic differential equations from Eq. using the Fuler-Maruyama
method (Higham 2001). Since tg and t, are sampled independently (as discussed in Sec. (.2.2). the
model allows the exploration of different paths going from (tg, (x) (0, 0) to (fz, fx) = (1, (that
is, different paths in the [o, 1) x [0. 1]. space). We parameterize these paths by defining t. = (t) and ts (t) using a shared time variable E [0. 1], where fz. [0. 1] - j0. 1] are monotonically Secs. and 3.4 using distinet schedules fz(() and (t)
increasing functions. As highlighted
for the a-carbon coordinates Xc., and latent variables z is critical for good performance. More specifically, our empirical analyses show that schedules evolving xc. faster than z yield the best results (sce App.Gr. G). We therefore adopt "exponential" schedule (Geffner et al. 2025) for (t) and a "quadratic" schedule for (t)
10-2 2
(a) = 1 - 10-2
and fz(1) = 12,
(11)
visualized in Fig. 32
The corresponding numerical integration scheme is obtained by uniformly partitioning the interval E [0, 1] (i.e., in = nn/N for n 0,1, yielding the discrete steps
tm/m= = fa(t)) = 1 10-2n/N
12 N
and [=[m] = f=((tt) =
(12)
1 1 10-2
Ablations for different choices of [1)() and (2( are presented in App. we use = 400 integration steps.
G
For all our experiments
F ATOMISTIC MOTIF SCAFFOLDING
For atomistic motif scaffolding we included two different tasks: all-atom motif scaffolding and tip-atom motif scaffolding. For all-atom motif scaffolding, for a certain selection of residues (the motif) information about backbone position, side chain positions as well as amino acid identity is provided and the task of the model is generate For tip-atom motif scaffolding, the provided information includes only the amino acid identity as well
protein that includes this motif as part of it.
"Most existing generative models for protein design rely on some variant of low temperature sampling
Ingraham et al. [2233] Yim et al. (2023b a Watson al. 2023 Lin et al. 2024 Bose al. 2024 Wang al.
2024a Huguet 2024 Campbell 2024 Geffner 2025).
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Simuiation time [(n)
0.0.
0.6-
0.4
Exponential
Uniform
Quadratic (t,)
30
100
150
200
250
300
350
400
Simuuation step
Figure 32:
Discretization schemes, including uniform reference.
as the coordiantes of the side chain atoms after the final rotatable bond. This means the following atoms made available for the respective amino acids, following the task definition of Protpardelle (Chu et al. 2024):
ALA:
{CA, CB}
ARG:
{CD, CZ, NE, NHI, NH2)
ASP:
{CB, CG, OD1, OD2}
ASN:
{CB, CG, ND2, OD1}
CYS:
{CA, CB, SG}
GLU:
{CG, CD, OEI, OE2)
GLN:
{CG, CD, NE2, OE1}
GLY:
0
HIS: {CB, CG, CD2, CEI, ND1, NE2}
ILE: {CB, CG1, CG2, CD1}
LEU: {CB, CG, CD1, CD2)
LYS: (CE, NZ)
MET:
{CG, CE, SD}
PHE:
{CB, CG, CD1, CD2, CE1, CE2, CZ)
PRO:
(CA, CB, CG, CD, N}
SER:
{CA, CB, OG}
THR:
{CA, CB, CG2, OG1}
TRP:
{CB, CG, CD1, CD2, CE2, CE3, C72, CZ3, CH2, NE1)
TYR:
{CB, CG, CD1, CD2, CE1, CE2, C7, OH)
VAL: (CB, CG1, CG2)
We also evaluate two distinct scaffolding setups that differ in their conditioning information. In the standard indexed task, the model is provided with the sequence positions for each motif residue. In the more challenging unindexed task, these indices are withheld, requiring the model to discover viable placement for the motif while simultaneously generating the scaffold.
F.1 TRAINING
We train the motif scaffolding models following the same training procedure as for the main models, with additional input features extracted from the motif. In the case of all-atom motif scaffolding, these features include (for the motif's residues) absolute atomic coordinates, coordinates relative to the corresponding a-carbon atom, residue type. side chain angles, and backbone torsion angles. For tip-atom motif scaffolding, these features only include absolute atomic coordinates of the atoms present in the motif (i.e. atoms after the last rotatable bond) and residue type. For the indexed version,
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Table Motif data with minimum and maximum lengths, and contig strings (all atom and tip atom).
Motif Name
Min Length
Max Length
Contig String
Atom
Contig String
IPRW AA
60
105
5-20AA 20000-0-210--//11111 10001002//1-205----- 1-205-00
5:30AA6-22/1A222//AAAA 52/11/4-
35/10 25/A52 58/1 1//6// A62-7122222
20
AB
96
8-15/A92-99/1--300333 12- 10016-
8-15/992-66/1 1/39 288--99777777 99-66-3044 36-30A
25/8-15
3TPN AA
50
10-10AA166-11710-4000
10-40VAT66-1877000
SAUS_AA
57
142
0-30/8119:18 5-40/66--220--00
1-31/A120-11
2011/112-12///// 123/1/11221555 1--1 NOYIA
140/15 40/66-00/333/// 111---77///7--200000
AX
50
10-401154-2777000-
SYULAA
50
100
S.3IN99199755- 2109--977/--81111
12VT0-
F.30/A93397755200 20A.TTIITT.. 120-0
35/C198-200/10 200010000
20-000000-30
SAQU
230
270
40-60VNTOST/ 21111///00002200810000
15/A2110/100. 140
35/A21 100 (00- 140
3ADU_QUAD AA
230
18/4211060-88 20AA21804AAI 80440-60
35/A21 800600000--22-- 20V440006
TK4V AA
280
320
205:5//444/ SAA///-//AA S/A30 70-8000-88/1111 27/100
80-50/A4-775- 7050770--5A
A 577
TYCR AA
40
100
10-40V819-37/10-1
10-10819-27/100
UHW
60
10
10-15/196 11715-3008 36T63 69/10
SWN9 AA
35
10-10NA 189/10-10
10-10VA170 1881/188-11888 189/10-10
4ZYF
30
30
10. 40A42222 436/T0-40
TO-4XA422 ESTTAATT TA
AVWI
20-30/A24-1244 101-1-122-11066--2000000
20-30/A24- 10VA61-65///66.
8200-5
TQKI_A
53
103
10-30/11//15 30000
AM
115
10 NAXAAAAASS33AA33300000000
10-20A1415 30A3000 70A99923.
30
30
2KL3 AA
79
79-720V228-79
A1-1/N0A28-79
1MRX AA 60
60
D- 30/1 1832242/11111 4014-
MMRX AA
83
0-63/825-
(-63/B25 111--3
7MRX 128
128
0-122/825-460 4000125-4/0-122
21122/22-300118880 122
STRV_AA WAW_AA_STORI
56
(335/4456550-35
1.36446 48/ 41710005555
(W1/A61-6500-
STRV_AA AA
MED MED
86
86
0185/A45-550065
1-66/446 48/16 491//50 35/1/A3
59/1/A61 65/0-66
STRV LONG
116
0:93/A/5-6500-99
1-9A/16-18/88
59/1/A61 65/0-95
NAR SHORT
48
0-55/A24-550-35
(-/8//23- A-15/A23-52//A3411 32/11311111
6E6R AA, MED
78
0-65/N23.35/0665
0.65/A23-32/1/34411
MAR AA LONG
108
108
0-99/22--350-95
0-99122--2///33441-36
these features are added to the corresponding residue indices of the motif; while for the unindexed task they are concatenated the initial sequence representation without providing any information related to the motif residue indices to the model. The dataset used was the standard dataset used for training the main models, i.c. the Foldseek-clusters of the AFDB with a maximum length of 356 and minimum average pLDDT of 80. The indexed all-atom motif model was trained for 150k steps on 64 NVIDIA 1000-80G GPUs, and the indexed tip-atom motif model was trained for 120k steps on 128 NVIDIA A 100-80GB GPUs. The unindexed models (all-atom and tip-atom) were trained on 32 NVIDIA A100-80GB GPUs for 650k steps.
F.2 SAMPLING
For sampling, the standard sampling schedule of the main models was used (App- D The motifs were sampled according to the specifications in the Protpardelle benchmark/FFDifttsioon benchmark, with the only difference being that for tip-atom motif scaffolding the residues that did not include any atoms to be scaffolded (Glycine, or Lysine if the tip atoms specified in the description were not present in the motif structure) were excluded from the motif. This resulted in the definition of benchmark tasks in Table
F.3 EVALUATION
We evaluate each generated sample via four criteria:
1. The sequence of the motif has to be 100% recovered,
2. The motif o-carbon coordinates should have all-atom RMSD <1,,
3. The motif coordinates should have all-atom RMSD <2Å,
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All-Atom Motif Scaffolding
Tip-Atom Motif Scaffolding
10.
1 vagganii
Pangmeri
regmenee
2 cegmentt
soggnonn
202
Unique Successes
100
20+
10
100
dere CoNe ne Sraw Lund
GEGA gtcon 3 pei soiee to
Sith SMOU DEAO
STAY CONO SThe MED LONG
aeoi forr tiie df
do
so SAMU INCA
STRe
Propperdele-Ir (ndesed, geserated stracture mvll)
La-Phttetn (indeced, generated structure mvnD
La-Proteina (urtrdeodd, generated strurture
(indesedd
woal)
Figure 33: Atomistic motif scaffolding using generated vs. refolded structures. 26 atomistic motif- scaffilding tasks (x-axis), comparing Protpardelle-Ie Ic (limited all-atom indexed), La-Proteina (indexed) and Ca-Proteina (unindexed). Solid markers indicate performance when evaluating the model produced structures directly (App. while light markers indicate performance when performing the evaluation using refolded structures instead of the model generated ones (App. F.4. "# segments" refers to the number of residue segments in the motif.
4. The generated protein should be all-atom co-designable, i.c., it should have have an all-atom scRMSD <2A.
For all methods we generate 200 samples per task. We then evaluate these samples via the criteria above, which results in the number of successes per task. Finally, the number of unique successes is obtained by clustering the successes with Foldseek (yan Kempen et al. 2024) and reporting the number of clusters. We use the following command to cluster:
foldseek easy-cluster <path_samples: <path_tmp>/ /res <path_tmp> aaaaannnenttttye type 1 --co-mmode -tmscore-thresholl 0.5 --single-stepp-custee
min--eq-id
The full results for all methods can be found in Table B for all-atom motif scaffolding and in Table for tip-atom motif scaffolding. Results show that La-Proteina outperforms both Protpardelle and Protpardelle-Ie lc. Additionally, we observe that Protpardelle able to solve 4/26 tasks both the all-atom and tip-atom setups. This is consistent with the findings reported in the original Protpardelle paper (Chu et al., 2024); our evaluation criteria, as outlined above, align closely with their "strict" definition of success, under which they also report limited task success. While they additionally report results under more lenient "weak" success criterion, we emphasize that this criterion is easier to satisfy than both their strict definition and our own. Notably, our model already achieves strong performance under the stricter standard, underscoring its robustness even under more challenging evaluation settings.
Note on indexed vs. unindexed evaluation. Evaluating motif accuracy via RMSD differs signif- icantly between the indexed and unindexed scaffolding tasks. In the indexed setting, the motif's sequence indices are known, making the RMSD calculation a straightforward comparison between the known motif residues of the ground truth and generated structures. For the unindexed task, however, these residue indices must first be inferred from the generated output. We address this by employing a greedy matching procedure (Chen et al., (025): for each residue in the ground truth motif, we identify its structurally closest counterpart in the generated protein. The motif RMSDD is then calculated using this newly identified set of residues. Because the model may place the motif at different sequence positions in each sample, this matching process must be performed independently for every generated protein.
F.4 EVALUATION VIA REFOLDED STRUCTURES
In addition to evaluating the directly generated structures, we conduct an alternative validation by analyzing refolded structures. To this end, take the sequences produced by each model (La-
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Table 3: All-atom motif scaffolding. "All" indicates total number of successes produced by the model (we produce 200 samples per task), while "Unique" indicates number of unique successes, obtained by clustering all successes as explained in App. F33 "Indexed" indicates the motif residue indices are provided as input to the model, "Unindexed" indicates that the motif residue indices are not provided input. "# segments" refers to the number of residue segments in the motif.
Motif Task
segments
Protpardelle (indexed) Protpardelle-Ie Te (indexed)
La-Proteina (indexed)
La-Proteina (unindexed)
Unique
Unique
Unique
Unique
6H6N, AA, long
D
16
14
91
53
110
83
18
92
55
96
64
IYCR AA
34
123
STRV AA long
D
20
78
20
84
39
7MRX A2_128
0
55
13
26
GEAR shon
STRY AA_med
0
68
16
STPN AA
0
16
49
28
7MRX
SIXT AA
4ZYP AA
0
7
65
STRV short
19
7MRX
SWN9 AA
0
0
IPRW AA
2
0
162
20
174
18
120
11
AA
6VWLM LA
0
23
70
2KL8 AA
2
80
177
119
193
JJHW
IQIG AA NAT
3
0
17
62
109
71
7K4V AA
3
0
18
47
SAOU
IQIG
50
16
SYULAA
0
16
SAOU AA
IBCF
147
147
12
Proteina and Protpardelle-1c), predict their structures using ESMFold, and then re-evaluate their success. In short, in this case the success criteria is given by
1. The sequence of the motif has to be 100% recovered,
2. The motif a-carbon coordinates should have an all-atom RMSD <1Å when comparing the refolded structure, obtained by running ESMFold on the La-Proteina produced sequence,
3. The motif coordinates should have an all-atom RMSD <2 when comparing to the refolded structure,
4. The generated protein should be all-atom co-designable, i.e., it should have have an all-atom ScRMSD <2'.
The results of this refolding analysis for all-atom and tip-atom motif scaffolding are presented in Fig. 33 Tab. [ and Tab. 6 We do not include Protpardelle in this more stringent evaluation as its performance is not competitive with La-Proteina and Protpardelle- lc. From the results, it can be observed that La-Proteina yields state-of-the-ar performance under this evaluation as well.
F.5 BASELINE SAMPLING
We sampled Protpardelle (Chu et al., 2024) (limited to indexed scaffolding) we used the option - -type alla allatom om and generate template pdb files with the motif coordinates as well as template residues for representing the scaffold in order to represent the correct length sampling ranges. For Protpardelle-Ic 1c (Lu et al.] 2025) (limited to all-atom indexed scaffolding) used the samples generated by the authors, as they evaluated their model on the same motif scaffolding benchmark, and we processed the samples using our evaluation pipeline.
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Table Tip-atom motif scaffolding. "All" indicates total number successes produced by model (we produce 200 samples per task), while "Unique" indicates number of unique successes, obtained by clustering all successes as explained in App. F.3 "Indexed" indicates the motif residue indices are provided as input to the model, "Unindexed" indicates that the motif residue indices are not provided input. "# segments" refers to the number of residue segments in the motif.
Motif Task
segments
Protpardelle (indexed)
La-Proteina (indexed)
La-Proteina (unindexed)
All
Unique
All
Unique
All
Unique
IYCR AA
0
112
54
109
47
STRV_ SERV_A__loo Ao_long
0
75
16
66
42
STRV _A__med
0
41
14
67
33
6E6R AA_ long
0
30
12
17
13
AA
0
96
13
STPN_AA
0
20
10
4ZYP
STRV_AM BOY_AAA_hhrr
14
6E6R AA
35
6E6R AA short
0
16
5WN9_AS
0
7MRX AA A2_
0
44
22
7MRX AA_85
0
72
7MRX AA 60
0
1
JJHW AA
2
0
0
6VWLAA
2
0
28
63
IPRW AA
2
2
45
25
SIUS AA
2
0
1
2KL8 AA
2
6
189
154
IQIG AA NAT
3
0
109
37
85
78
7K4V AA
3
0
28
27
68
64
IQI AA
3
2
125
51
61
55
DAOULAA
3
0
64
16
43
40
SYULAA
3
0
3
SAOU_QUAD QUAD_AA
4
0
95
35
29
IBCF_A AA
4
42
152
10
146
10
G ABLATIONS
G.1 VAE ABLATIONS
We first ablate multiple choices in the VAE's design: The weight use for the KI. term in the ELBO loss from Eq. (3) the architecture type used for the decoder, and building fully-latent model that encodes a-carbon coordinates well (in contrast La-Proteina, which models a-carbon coordinates explicitly).
G.1.1 KL PENALTY WEIGHT
KL-weight. The weight use for the KL term in the ELBO loss from Eq. (3) for which tested values {10 -3 3,10 1,10-5).
G.1.2 DECODER ARCHITECTURE
Decoder arch. The type of architecture used for the decoder, for which we compare the transformer used by all our models evaluated in the main text, against using a feed forward network with 7M parameters. For this we weight of 10-5 for the KL term in the ELBO loss from Eq. (3).
G.1.3 ENCODING a-CARBONS
CA-enc. We test encoding the a-carbons as well (with transformer decoder). In this case, the a-carbon coordinates not modeled explicitly, in La- La-Proten,a, but also encoded into the eight- dimensional latent space. This ablation shows the importance of explicitly modeling the a-carbon coordinates. For this weight of 10-5 for the KI. term in the ELBO loss from Eq. (3).
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Table 5: All-atom motif scaffolding, evaluation with refolded structures. "Evaluation using refolded structures" indicates that a success is given by the criteria specified in App. F.4 which compares refolded structures where the sequence is produced by La-Proteina and then folded with ESMFold-aaaee against the motif (instead of comparing the generated structure directly, explained in App. F33
"All" indicates total number of successes produced by the model (we produce 200 samples per task), while "Unique" indicates numher of unique successes, obtained by clustering all successes as explained App. F33
"Indexed" indicates motif
residue indices are provided as input to the model, "Unindexed" indicates that the motif residue indices are not provided as input. "if segments" refers to the number of residue segments in the motif.
Evaluation using refolded structures
Motif Task
# segments
Protpardelle-Ic (indexed)
La-Proteina (indexed)
La-Proteina (unindexed)
All
Unique
All
Unique
All
Unique
AA Aong
13
12
84
52
97
72
GE6R_A. AA, med
18
17
78
47
87
59
IYCR AA
56
29
117
37
91
S1
STRV AA long
5
36
7MRX AA_ 128
2
9
42
GEGR AA, short
26
18
44
22
STRV AA med
25
8
27
12
STPN AA
25
7MRX 85
25
3IXT_A
21
49
4ZYP AA
4
27
STRV short
7MRX
49
AW
IPRW AA
2
162
20
174
18
120
10
SIUS AA
2
0
1
6VWL AA
2
11
22
42
2KL8 AA
2
51
4JHW AA
2
0
QQI AA NAT
3
23
50
7K4V AA
3
2
33
4
29
29
SAOU AA
3
39
5
157
9
11
11
IQIG AA
3
4
29
23
SYULAA
SAOU QU
12
17
IBCF
4
195
6
144
89
G.1.4 RESULTS
For each VAE variant, we train a dedicated flow matching model using the Foldseek clustered AFDB dataset (filtered to maximum protein length of 256 residues). We then evaluate the generative performance by measuring all-atom co-designability and diversity on proteins sampled at lengths of (50, 100, 150, 200, 250}. ). We use the sampling hyperparameters detailed in App. E for the KL-weight and Dec-arch VAE variants. However, this setting is not directly applicable to the CA-enc model, as it encodes the entire protein, including o-carbon coordinates, into its latent variables and does not explicitly model ax-caroons separately. To ensure a fair comparison and optimize its performance, we conducted hyperparameter search for the CA-ene model. This involved exploring both Langevin scaling functions ("1/t" and "tan" from Eq. (10)) and all three numerical discretization schemes ("exponential", "uniform", "quadratic" from App. best results.
and selected the combination that yielded
The results from this VAE ablation study are shown Tab. which reports all-atom co-designability and diversity values for each model. The three main conclusions are: First, Lower weights for the KI. divergence term in the ELBO objective (10-4 and 10-5) yield better generative performance than higher weight (10-3). Second, replacing the transformer architecture in the decoder by feed forward network (7M parameters) leads to worse performance, Third, and most critically, explicitly modeling a-carbon coordinates, cornerstone of La-Proteina's design, leads to substantially better results than an approach that encodes the entire protein structure, including a-carbon coordinates, into unified latent space (as in the CA-ene model). This last finding is particularly relevant, as strongly validates La-Prot Proteina's 's fundamental design choice treating the a-carbon backbone explicitly, rather than relying on fully latent representation for the whole protein structure.
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Table 6: Tip-atom motif scaffolding, evaluation with refolded structures. "Evaluation using refolded structures" indicates that a success is given by the criteria specified in App. F.4 which compares refolded structures where the sequence is produced by La- La-Proteina and then folded with ESMFold-aaae against the motif (instead of comparing the generated structure directly, explained in App. H33
"All" indicates total number of successes produced by the model (we produce 200 samples per task), while "Unique" indicates number of unique successes, obtained by clustering all successes as explained App. F33
"Indexed" indicates motif
residue indices are provided as input to the model, "Unindexed" indicates that the motif residue indices are not provided input. "if segments" refers to the number of residue segments in the motif.
Evaluation using refolded structures
Motif Task
# segments
La-Proteina (indexed)
La-Proteina (unindexed)
All
Unique
All
Unique
IYCR AA
111
54
45
5TRV Ao__ong
46
13
29
23
STRV B___AAA_m_ med
19
10
20
12
6E6R AA long
28
12
8
7
3XT AA
94
11
STPN AA
7
4ZYP AA
6
5TRV AA_short
2
0
6E6R AA med
30
5
2
2
6E6R AA short
16
5
2
5WN9 AA
0
7MRX AA 128
18
7MRX AA 85
39
3
0
7MRX_AA_66 AA_60
0
0
0
4JHW AA
0
0
0
6VW1 AA
2
19
2
61
4
IPRW AA
2
45
5
25
3
SIUS AA
1
0
2KL8_AA
77
IQIG_AA_NAT
3
38
18
18
18
7K4V AA
12
12
15
15
IQJG AA
67
15
5AOU AA
52
8
18
SYUL
3
3
SAQU QUAD_AA
29
IBCF AA
145
10
132
10
Table Ablation study the VAE design, including different weights the KL, penalty term, a variant of the VAE which uses feed forward network instead of the transformer in the decoder, and a variant that also encodes the a-carbon coordinates (that is, in this specific case, the flow matching model operates entirely in the latent space, without explicitly modeling c-carbon coordinates, which also captured by the latent variables). flow matching model on proteins of length up to 256 residues and report co-designability diversity metrics. All models were evaluated for multiple noise scaling parameters, and we selected the one that led to the best performance (not reported for simplicity).
VAES
VAE Type
KL weight
Co-designability (%)
Diversity (# clusters) f
All-atom
Str
Sey
Sey
Str
Transformer (enc), Transformer (dec)
10
65.2
154
163
248
Transformer (ene). Transformer (dec)
10
83.8
246
317
374
Transformer (ene), Transformer (dec)
10
82.4
214
295
339
Transformer (enc), Feed Forward (dec)
10
58.0
151
242
233
Transformer (enc), Transformer (dec), encode a-carbons
10
21.2
51
105
91
G.2 FLOW MATCHING SAMPLING HYPERPARAMETERS
As explained in Sec. 3.4 and App. sampling La- Proteina requires selecting the discretization scheme used for the c-rabo coordinates xc,, and latent variables z, and the functions to scale the
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Table 8: Ablation study over discretization scheme Langevin term scaling functions La-Proteina sampling. The table includes combinations that yield an all-atom co-designability of at least 0.5. Details for
the different discretization schemes and Langevin scaling functions are given in App. B computed over the subset of all-atom co-designable samples.
The diversity metric is
Method
Discretization
Langevin scaling
Noise sculing
Co-designability
Diversity (# clusters)
a-curbon
Latent
B,(t,)
B.(t,)
Tr
All-atom
Str
Sey
Seq Str
La La-Proteina
exp.
quad.
1/t
0.1
68.4
206
216
310
La Proteina
exp.
quad.
1/t
tan
0.2
0.1
60.6
198
197
261
La- ProPeitn
exp.
quad.
1/t
tan
0.3
0.1
53.8
180
189
249
La-Proteing
exp.
quad.
1/
1/t
0.1
0.1
59.2
164
198
247
La- La-Proteina
exp.
quad.
1/
1/t
0.1
0.2
57.0
163
189
253
Pa-Protiina
exp.
quad.
1/t
1/t
0.1
53.4
190
191
La La-Proncina
exp.
unif.
1/t
1/1
0.1
0.1
50.6
194
189
226
La Pr-Prrtenna
exp.
unif.
1/
tam
0.1
0.1
$4.0
210
197
247
La-Proteina
exp.
unif.
1/t
tan
0.2
0.1
52.4
208
185
246
La- La-Proteina
exp.
quad.
lan
1/t
0.1
57.0
161
212
La Pr-Prennn
exp.
quad.
1/t
0.1
53.6
171
203
244
La Ca-Proteina
quad.
tan
tam
0.1
0.1
57.4
168
217
251
ProPPrteina
exp.
quad.
tan
tan
0.1
0.2
55.4
183
216
252
Langevin term in the SDE from Eq. 7 As a brief reminder, App. D introduced three discretization schemes, "exponential", "quadratic" and "uniform"; and also two scaling functions for the Langevin term in the SDE, the "I/t" and "tan", shown in Eq. (O).. While our primary La-Proteina configuration (evaluated in Tab. [T uses specific pairing (namely, "exponential" discretization with "1/t" scaling for the a-carbon coordinates, and "quadratic" discretization with "tan" scaling for the latent variables), alternative combinations are viable. To systematically assess how these choices affect performance, conducted ablation study by sampling specific variant of La-Proteina (the model from Sec. f without triangular multiplicative layers) with all possible combinations of these schemes and functions for generating both the a-carbon coordinates XC. and the latent variables z.
The outcomes of this ablation are presented in Tab. 8. which includes hyperparameter combinations that yield an all-atom co-designability of least 0.5. A clear pattern emerges from these results: only sampling configurations that generate a-carbon coordinates at an effectively faster rate than the latent variables surpass the 0.5 all-atom co-designability threshold. More specifically, every successful combination listed employs the "exponential"" discretization scheme for XC, using either the "quadratic" " or "uniform" scheme for This implies that other pairings, such as applying "quadratic" or "uniform" schedules for XC., or the "exponential" schedule for did not yield competitive co-designability values. While the choice Langevin scaling function also influences performance, its impact was observed to be less pronounced than that of the discretization scheme.
G.3
MAIN CONCLUSIONS FROM ABLATION STUDIES
The primary conclusion from our ablation studies is that achieving strong performance critically depends on key factors: first, the explicit modeling of a-carbon coordinates, and second, generating these coordinates at an effectively faster rate than the latent variables (which encapsulate all remaining atomic and sequence details).
H ARCHITECTURES
The three neural networks used in La-Proteina, the encoder, decoder, and denoiser, rely on the same core architecture based on transformers with pair-biased attention mechanisms (Jumper et al. 2021 Abramson et al,, 2024). Our implementation closely follows Geffner et al. (2025), to which we refer for comprehensive details. This architecture processes inputs into two primary tensors: a sequence representation of shape [L, Cseg]. which encodes per-residue features (e.g., atomic coordinates, residue type, etc.), and pair representation of shape [L, L, Cpair], which encodes features between residue pairs (e.g., relative sequence separation, inter-residue distances, etc.). The sequence representation is iteratively updated through the transformer blocks, while the pair representation provides biases to the attention logits via a learned linear projection within each block, effectively incorporating relational information (Jumper al. 2021). As aforementioned,
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explore two variants for the denoiser network. One that keeps the pair representation fixed throughout the architecture, and one where we use triangular multiplicatiie update layers to update the pair representation, including one such layer every two transformer blocks (Jumper et al. 2021). While these updates have shown performance gains in complex structural biology tasks (Lin et al. 2024 Jumper al., [02T]] Abramson et al. (024), they also add considerable computational expense. Most La-Proteina models we evaluate do not use triangular update layers and yield state-of-the-art performance. In practice, we use C'seq 768 and Cpair 256, 14 transformer layers for the encoder and decoder, and 16 layers for the denoiser, yielding a total of 130M and 160M parameters, respectively.
The primary distinction between our three networks lies in the specific inputs they receive, how these inputs are featurized to construct the initial sequence and pair representations, and the target outputs they predict. The feature construction follows closely closely|McPartton McPartlon & Xu (2023). The sequence representation captures features for each independent residue (e.g. atomic coordinates), while the pair representation captures features for residue pairs (e.g. relative distance and sequence separation).
Encoder. The encoder parameterizes the Gaussian distribution ga X-CC,, Xc..). mapping the inputs (xc,, ,)) to the distribution's 's mean E RL8 and log-scale log E RLx8 The input features used by the encoder to construct the initial sequence representation are: (i) Raw absolute Atom37 coordinates; (ii) Raw Atom37 coordinates, relative to the a-carbons; (iii) Residue type, as a one-hot vector; (iv) Side chain angles, consisting of at most four angles (depends residue type), which are binned into 20 bins between -π ग and π.; (v) Backbone torsion angles, which are binned into 20 bins between- - and π. The input features to construct the initial pair representation are: (i) Relative sequence separation, as one-hot vectors, capped at 164; (ii) Relative orientations between pairs of residues Yang et al. (2000), which are binned into 20 bins between IT and π, (iii) Pairwise distances between a-carbons and all other backbone atoms, binned into 20 bins between IÅ and 20A. The initial representations are then processed through 12 transformer blocks. The final sequence representation is fed through a linear layer to produce and log o, and the latent variables are obtained as z ~ N(u, o²) E L
Decoder. The decoder parameterizes the Categorical distribution P z, xC.) and the Gaussian distribution (x-c.. z, xc.), mapping the inputs (z, Xc.) to the logits of the Categorical, ! E R4x20, and the mean of the Gaussian, /idee E RLx36x3 (variance fixed to one). The input features used by the decoder construct the initial sequence representation are: (i) Raw a-carbon coordinates Xc,; (ii) Raw latent variables z. The input features to construct the initial pair representation are: (i) Relative sequence separation, as one-hot vectors, capped at 64 (ii) Pairwise distances between a-carbons, binned into 30 bins between I and 30A. The initial representations are then processed through 12 transformer blocks. The final sequence representation is fed through a linear layer to produce and plee.
Denoiser network. The denoiser network maps time-dependent inputs, the interpolation times tz, and corrupted coordinates x and latents z²= to velocity fields v E 4x3 and v3. E Rxx8 used to sample (xc... z)). The corrupted inputs are featurized into the initial sequence and pair representations. More specifically, the initial sequence representation uses: (i) Raw corrupted a- carhon coordinates x²= (ii) Raw corrupted latent variables z'= The input features to construct the initial pair representation are: (i) Relative sequence separation, one-hot vectors, capped +44 (ii) Pairwise distances between corrupted o--carbon coordinates, binned into binned into 30 bins between 1 and 30Å. The initial representations are then processed through 14 transformer blocks. The final sequence representation fed through linear layer to produce vž and vg. In contrast to the encoder and decoder architecture, the denoiser network also conditions on the interpolation times l and lg. This is done directly within its transformer blocks using adaptive layer normalization and output scaling techniques (Peebles & Xie 2023).
1 MODEL PARAMETERS, SAMPLING SPEED AND MEMORY CONSUMPTION
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Table 9: Sampling time [seconds] different methods at batch size (top) and maximum batch size (bottom) across varying protein lengths on an A100-80GB GPU. For PLAID and La La-Proteina, the first parameter count the diffusion model and the second one is the decoder.
Method
Params
Steps
100
200
300
400
500
600
700
800
Batch size:
P(all-atom)
17.7M
200
32.9
62.1
106.1
0OM
OOM
OOM
0OM
0OM
ProteinGenerator
59,8
197.8
239.6
428.6
642.8
981.0
1365.4
1915.0
2690.4
Protpardelle
25.1M
200
2.3
3.2
4.3
5.2
6.1
7.3
8.4
9.5
PLAID
100M 3.5B
500
6.2
8.0
11.6
18.1
25.4
38.1
54.4
77.6
La-Proteina
158M 128M
400
2.94
3.00
3.67
4.75
6.33
8.45
10.63
13.52
La-P La-Proteina
167M 128M
400
4.22
9.72
20.78
34.85
59.95
100.00
153.14
196.46
Maximum batch size (runtimess normalised to be per sample; batch size values in Table 70
PLAID
100M 3.5B
500
0.78
3.16
7.29
15.00
22.55
36.75
54.33
78.17
La-Proteina
158M 128M
400
0.34
0.99
2.04
3.34
5.01
7.01
9.46
12.31
La-Proteina tei
167M 128M
400
1.72
6.31
16.29
25.74
42.45
59.28
77.38
106.69
Table 10: Maximum batch size samples of varying length (the numbers the top row indicate protein backbone chain length) on an A100-8000 GPU.
Method
# Model parameters
Inference steps
100
200
300
400
500
600
700
800
PLAID
100M + 3.5B
500
154
73
20
La-Proteina
158M 128M
400
422
118
49
17
La-Proteina tri
167M 128M
400
530
150
60
22
10
To evaluate both model complexity (through parameter counts) and its operational consequences for memory usage and generation speed, we perform three complementary experiments following Geffner et al. (025):
1. Single-sequence inference latency: Measurement of per-sample generation time using batch size on an NVIDIA A A100-80GB. Results appear Table Duller part.
2. Batch-optimized throughput analysis: Measurement of generation times at maximum batch capacities, with computational efficiency quantified through time-per-sequence nor- malization. Executed on A A100-80GB GPUs as documented in Table l part.
3. Memory efficiency assessment: Determination of maximum viable batch sizes without exceeding memory limits, conducted on an NVIDIA A A100-80GB GPU to establish practical scalability thresholds. See Table 10 for detailed comparisons.
All referenced tables include parameter counts for cross-model comparison.
Our implementation capitalizes on the transformer architecture's hardware compatibility through PyTorch's compilation framework (Ansel et al., 2024), which accelerates both training and inference phases. Reported inference metrics for La-P Proteina as well as other models leveraging compilation such as P(all-atom) reflect performance optimizations achieved via model compilation and report timings excluding compilation overhead at the beginning since it becomes negligible for large-scale inference which is mostly of interested the protein design setting.
We can see that La- La-Protei is fast despite the high parameter count; the model without triangle multiplication layers is the fastest togther with Protpardelle. The model with triangle multiplication layers is slower, but still faster than P(all-atom) and Protein Generator, as well as faster than PLAID at short lengths.
Since only La-Proteina and PLAID support batched inference, the difference becomes stark there: at maximum batch size La-Pre Proteina can generate hundreds of proteins one batch, resulting in inference times of below second for short proteins. Interestingly, after compilation of these models the models with triangle multiplication layers is able to fit higher batch sizes than the one without triangle multiplication layers, probably
artifact of the compilation process.
One also sees the La-P Proteina benefits a lot more from batched inference speed-ups than PLAID. This is mostly due to the La- La-Proteina decoder being fairly lightweigth and fast, with the majority
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Table 11: Novelty results for Foldseek 10.94 10.941cd33. Should be contrasted to results Tab. which uses Foldseek version 9.427dr8a (included in the table for reference).
Method
Novelty (Foldseck 10.941cd33)
Novelty (Foldseck 9.427dfSa, reference from Tab
PDB
AFDB
PDB
AFDB
Plall-atom)
0.79
0.86
0.72
0.81
Protpardelle-Ic
APM
0.88
0.92
0.84
0.89
PLAITD
0.92
0.94
0.89
0.92
ProteinGenerator
0.87
0.92
0.83
0.89
Protpardelle
0.82
0.85
0.79
0.82
La-Proteina (Nz. Rt) (.11
0.81
0.86
0.75
0.82
(tte [b] (0.2, 0.1)
Lo-Proteina (Re.)t.) Rt)) (0.3,0.)
0.82
0.87
0.77
0.86
Proteina ni (/te (.) (0.1.0.1)
0.9
Lo Lo-Proeeina (Ate)1t)) (0.3,0.1)
0.83
0.88
0.79
0.85
of time spent during the diffusion process, while in PLAID the ESMFold-3B decoder is the major bottleneck.
J ADDITIONAL RESULTS
J.1 NOVELTY RESULTS WITH NEWER FOLDSEEK VERSION
Tab. in the main paper reports novelty results using Foldseek version 9.427df8a. We note that newer Foldseek versions return different values for the exact command and samples. Tab. [1 shows novelty results for all methods using Foldseek version 10,941cd33. The table only reports novelty values, all other metries are exactly the same in Tab. D
J.2 UNCONDITIONAL EVALUATION ON SHORTER PROTEINS
To complement our main evaluation from Tab. we performed an additional comparative analysis using subsets of shorter proteins. This accounts for the diverse training distribution of various baseline models, some of which were trained on proteins shorter than those used to train Lu-Proteina. We assessed all models across three scenarios: (A) 100 proteins of length 100; (B) 200 proteins, with 100 samples each for lengths 100 and 200; and (C) 300 proteins, comprising 100 samples each for lengths 100, 200, and 300. The resulting all-atom co-designability and diversity metries for this analysis summarized in Tab, [2] where it can observed that La-Proteina yields state-of-the-ee performance across all three scenarios.
J.3 PLDDT VALUES
Violin plots showing the distribution confidence scores (pLDDT) for protein structures generated by La-Proteina and baselines are shown in Fig. 34| The samples used for those plots are the same as the ones used for the results in Tab. T filtered by all-atom co-designable, that is, we only include samples with all-atom RMSD between the model produced structure and the one obtained by folding the model produced sequence with ESMFold < 2A. The results show that all variants of La-Proteina different temperatures and with/without triangular update layers, consistently achieve the highest median and interquartile range (IQR) PLDDT values.
J.4 RESIDUE TYPE DISTRIBUTION
Fig. 35 shows the distribution of amino acids generated by each of the comparative methods against the UniProt reference distribution. The samples used for this figure are identical to those used for Tab. [ filtered by all-atom co-designability. As it can be observed from the figure, all methods over- and under-represent certain residues when compared against the UniProt reference distribution. Notably, demonstrated in Fig. [36] La-Proteina produces a distribution over amino acid types very similar to the ones produced by ProteinMPNN. We view this as a positive outcome, as sequences generated by ProteinMPNN are generally acknowledged possess highly desirable properties.
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Table 12: Results for unconditional generation for proteins different lengths. Table (A) shows results for proteins of length 100; table (B) for proteins of lengths in (100, 200), with 100 samples per length; table (C) for proteins of lengths in 1000 200, 300). with 100 samples per length. and y)s denote the noise scaling factors during generation (Eq.
Best scores for each table bold, second best underlined.
Method
All-atom co-designability
Diversity (# clusters) 1
Structure Sequence
Sequence + Structure
(A) 100 proteins for each length (100)
P(all-atom)
88.0
41
78
Protpardelle-Ie
76.0
13
67
APM
56.0
15
48
33
PLAID
22.0
14
18
15
ProteinGemerator
45.0
13
27
22
Protpardelle
29.0
26
La- La-Proteina (Ma, no) = (0.1,0.1)
96.0
43
89
82
La- Ka-Proteina (Na: No. (0.2,0.)
90.0
54
78
La-Proteina (Tle N1)) (0.3,0.) 0.1)
88.0
55
100 proteins for each length [100, 200)
P(all-atom)
80.5
111
132
Proipardelle-Ic
70.0
14
115
APM
38.0
24
48
56
PLAID
15.5
18
24
20
ProteinGemerator
26.0
14
26
26
Protpardelle
17.0
9
La-Proteina (ne, = (0.1,0.1)
89.5
93
147
151
Proteina (Ne N1. = (0.2.0.1) 0.1)
84.0
104
145
La-Proteina (Mt.) N1) 0.1)
80.5
111
146
100 proteins for each length [100. 200.300)
P(all-atom))
60.7
131
147
Protpardelle-Ic
58.3
14
133
APM
30.0
30
54
62
PLAID
15.3
23
32
25
ProteinGemerator
17.7
14
26
26
Protpardelle
14.7
36
La- La-Proteina (ne. no) = (0.1.0.1)
85.3
150
192
217
La-Proted Proteina (Ne Ne. = 0.12
77.7
144
181
198
Ca-Proteina (Ne: Ne) 0.13
69.7
139
173
The sequence results discussed above were obtained by our model using low temperature sampling, specifically with parameters (Nn, n2) = (0.1, 0.1). To quantitatively assess the effect of temperature parameters on the resulting sequence distribution, we generated 1000 samples length 100 using various temperatures. Results from this analysis increasing the temperature to 0.5 and 0.9 (for both backbone and latent variables jointly) leads to distributions that get increasingly closer to the UniProt reference. However, this increase in temperature comes at the cost of performance in other metrics, manifesting as reduced all-atom co- designability. For instance, across the samples produced for this specific temperature analysis, the all- atom co-designability decreases from 90% for (Me, 72) (0.1, 0.1), to 54% for (na Ma) = (0.5, 0.5). and finally to 11 % for (1=, n2) (0.9.0.9).
shown Fig. 37 where it can be observed that
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90
80
pLDDT
Percentile
25th Percentile
75th Percentile
60
95th Percentile
Median (50th)
Pallatom
APM
Gretror
PLAID
Protpardelle
La La-Proteina (f} n2) = 0.11,
Protpardelle1c
La La-Proteina (m, nu) (0.2. 0.1)
La- La-Proteina (n.. =2) (0.3, 0.1)
La La-Proteinau (m, (d) (0.1.0.1)
La La-Proteinan (0z nz)= (0.3, (0.3, 0.1)
Figure 34: La-Proteina samples with higher PLDDT than existing all-atom generation baselines. Samples
included in the analysis the same those to compute the metrics in Tab. [ As for most metrics (App. D we filter samples to keep only all-atom co-designable ones.
0.25
0.20
Frequency
0.15
0.30
0.05
0.00
ANG
ASM
ASP
CLR
TYR
Pallatom
Li-Proteinata
UniProt Reference
APM
ProteinGenerator
Protpardellelc
PaProteinay ()) (0.1. 0.11
Figure 35: Distribution of amino-acia acid frequencies of co-designable samples by different methods.
0.175
Frequency
0.125
0.300
0.000
0.025
ALA
ARG
ASN
ASP
CT5
GLM
(UU)
63
w6
118
180
055
MET
PME
SER
THR
TAP
TYR
VAL
(0.1,
MiNNN_ Www.U,,hhtaaaaeeeeaaaaaaa
UniProt Reference
Figure 36: Distribution of amino-acid frequencies of La- La-Proteina for different temperatures. Plots were obtained by filtering for co-designable samples.
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0.20
0.30
0.05
PLP
ASM
AsP
Ct5
GLN
GLU
G
4.8
685
MET
9Et
TRV
TYA
VM-
Proteina
0.5)
Proteina
(0.9,
Reference
Figure 37: Distribution of amino-acid frequencies of La-Pron Proteina for different temperatures. Plots were obtained by filtering for co-designable samples.
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K DECLARATION OF LARGE LANGUAGE MODELS USAGE IN THIS WORK
Large Language Models (LLMs) were used as a writing aid to enhance clarity and readability during the preparation of this manuscript. The use of these tools was strictly limited to grammatical correction and stylistic refinements. All intellectual content, analyses, and arguments in the paper did rely on the use of LLMs any way.
46


Reviews:
[{"review_id": "zrXyUbmZF5", "reviewer": "Reviewer_4Tcg", "summary": "This paper proposed a novel partial latent flow matching for full-atom protein generation. They encode varying-length side chains and categorical residue types into the latent space, and maintain the explicit $\\alpha$-carbon-based protein backbone representation in the coordinate space. They achieve SOTA performance on unconditional and conditional full-atom protein generation benchmarks.", "questions": "See Weaknesses.\n\n**Q1. Both equivariant rigidity-based methods like FrameFlow[1] or FoldFlow[2], or non-equivariant methods in coordinate space like Proteina or La-Proteina ($\\alpha$-carbon), all use a fast scheduler during the inference to ensure the quality of generated proteins. Do you have any insights or possible explanations for this phenomenon?**\n\n[1].Fast protein backbone generation with SE(3) flow matching\n\n[2].SE(3)-Stochastic Flow Matching for Protein Backbone Generation", "limitations": "", "rating": 10, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 4, "strengths": "The motivation is reasonable, proteins' natural hierarchical structure (backbone + side chains) and variable-length side chains are suitable for partial latent generation. \n\nThe method is presented clearly; training and inference hyperparameters are provided for reproducibility. \n\nThe experimental part is well-designed, and they achieve SOTA results on unconditional and conditional full-atom protein generation benchmarks. They also provide many ablation and analysis experiments to support their method.", "weaknesses": "**W1. The La-Proteina model has only been trained and tested on monomeric proteins. Can it be trained or fine-tuned on multi-chain data (protein complex design), such as APM[1]?**\n\n**W2. Folding can be regarded as a kind of conditional full-atom generation. Can La-Proteina compare on the folding benchmark?**\n\n\n[1].An All-Atom Generative Model for Designing Protein Complexes", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QCI2g69IWy", "reviewer": "Reviewer_duda", "summary": "This paper introduces La-Proteina, which addresses the protein codesign problem. La-Proteina tackles this via a \"partially latent\" representation. The C-alpha backbone coordinates are modeled explicitly, while the sequence identity and all other atomistic details are compressed into fixed-size, per-residue latent variables using a VAE. A scalable flow matching model that circumvents triangular update layers learns the joint distribution in this hybrid explicit-latent space. This also allows separation of generation processes for the coordinates and latents, which allows different generation schedules during inference. Empirically, La-Proteina achieves SOTA on co-designability and diversity benchmarks. The model also does well on long-sequence generation up to 800 residues. Additional conditional capabilities are demonstrated, including motif scaffolding without pre-specifying the positions.", "questions": "* AFAICT, the 8-dimension latent space does not report ablations. It would be interesting to better understand this dimensionality choice, especially considering the fact that we have some ground truth knowledge of the average number of atoms in a sidechain residue. Was this chosen based on ablations or intuition?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. Strong empirical performance across the board.\n2. Hybrid representation with the partially latent dimension is thoughtful. It allocates enough resolution to the key backbone portion while circumventing the issue of needing to pre-specify the number of atoms.\n3. Biophysical evaluations are compelling; examining for clash rates and rotamer frequencies sets a new evaluation metric that is meaningful for this subfield.\n4. The technical ability to decouple the timesteps necessary is thoughtfully designed, and the evidence for the argument that backbones require fewer inference timesteps than latent is illuminating.\n5. Unindexed motif scaffolding is a more meaningful conditional task, great to see it included.", "weaknesses": "* A short coming of having two noise schedules is that we now need to tune two noise schedules – authors were able to get good results regardless, but this is a small concern for practical usage.\n* Not so much specific to this paper, but generally conditional generation becomes much more interesting than pure unconditional generation. Would strengthen the paper if more of the work was focused on that aspect.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CS02UJPQsf", "reviewer": "Reviewer_UiFG", "summary": "La-Proteina introduces a partially latent flow matching framework for joint protein sequence and full-atom structure generation. The key idea is to model the protein backbone explicitly (using α-carbon coordinates) while encoding all side-chain atoms and sequence information in a fixed-size latent vector per residue. This hybrid representation avoids the combinatorial complexity of direct discrete side-chain modeling and enables powerful continuous generative dynamics on the backbone+latent space. The authors first train a VAE to map proteins (sequence plus structure) into the per-residue latent space and back, then train a flow-matching model (a form of diffusion) to jointly generate new backbone coordinates and latent vectors. They claim the following major contributions and results: \n\n**(1)** A novel partially-latent protein generative model that combines explicit backbone modeling with latent side-chain+sequence representation. \n\n**(2)** State-of-the-art performance on unconditional protein generation benchmarks, significantly outperforming prior methods in co-designability (ability to jointly fold sequence+structure), diversity, and structural quality. \n\n**(3)** Unique scalability to very long proteins: La-Proteina can generate plausible 800-residue designs where other all-atom models run out of memory or collapse (essentially failing beyond 500 residues). \n\n**(4)** Successful demonstration of fully atomistic motif scaffolding: given a small active-site motif (set of residues with known 3D arrangement), La-Proteina can build new proteins that accurately incorporate that motif. This holds even in the challenging “unindexed” setting where the motif’s position in the sequence is not specified. The model outperforms previous scaffolding approaches (which were limited to backbone-only or indexed placement) and solves most tasks in a standard benchmark. \n\n**(5)** Extensive analyses are provided: ablation studies show the importance of design choices, and structural evaluations indicate that La-Proteina’s samples are substantially more physically realistic than those of prior all-atom models.", "questions": "- How do you envision extending La-Proteina to design protein complexes or multi-chain assemblies? Since your current model represents one continuous chain with per-residue latents, would handling multiple chains simply be a matter of adding chain-break tokens or separate latent sequences per chain? Are there any obstacles (e.g. interfacing latents between chains, increased length) that you foresee? For instance, could the flow matching scale to, say, a heterodimer of 2×400 residues (total 800) as easily as a single 800-res chain?\n\n\n- Your training set of 46M samples is enormous. Did you observe how performance scales with fewer training examples or smaller models? For example, if only the PDB (~0.5M structures) were used, does La-Proteina still outperform baselines? Similarly, how crucial is the 130M parameter Transformer architecture? It would help to know if the method could work on more limited data/resources (perhaps with reduced output quality but still above prior methods). Any insight on the data efficiency (like learning curves) would be valuable for researchers who cannot train at that massive scale.\n\n\n- Have you tried a two-stage approach as a baseline, e.g., first generate a backbone with your flow model (ignoring latents), then design sequence/side-chains using an external model (like ProteinMPNN)? Essentially, how much do we gain by co-generating sequence and structure together, versus sequentially? Your results suggest co-generation is superior (given the high co-designability vs baseline designability), but a direct comparison would confirm the benefit of coupling. If not explicitly tested, what’s your intuition: is the improvement mostly because the model can adjust backbone positions to accommodate sequence mutations on the fly (something a sequential process can’t do)?\n\n\n- You report almost all samples are valid/co-designable and even tricky motifs are scaffolded well. Did you notice any recurring failure modes or patterns in the rare cases where La-Proteina fails? For example, in Figure 11 you show one inconsistency (a rotated ring) in a motif placement. Are such errors random, or do they happen more for certain residue types or structural contexts (e.g. certain ligand-binding motifs or β-sheet-rich motifs)? Understanding when the model struggles could guide future improvements. Additionally, during generation, do you ever get completely broken structures (e.g. chains that don’t fold into a single globule, or severe steric clashes)? If so, how do you detect or filter those? Overall the error rates seem low, but any insight into “edge cases” would be helpful.\n\n\n- Your diversity and novelty metrics indicate many unique structures are generated, but the average TM-score to known structures is ~0.75, implying the samples are still reminiscent of known folds. Can you provide qualitative examples of how novel the top designs are? For instance, have you found any new topologies (combinations of secondary structure never or rarely seen in PDB)? It would be reassuring to see that La-Proteina isn’t just reproducing common motifs in protein structure (like αα-hairpins, helix-loop-helix, etc.) but can also generate creative arrangements. If you haven’t assessed this, do you plan to? Perhaps tools like Foldseek or manual inspection could identify if any design is a true outlier relative to the training set. This will shed light on the model’s ability to extrapolate versus interpolate known protein geometry.\n\n\n- Following up on the lack of experimental tests, do you intend to collaborate or perform wet-lab validation of some La-Proteina designs? For example, taking a few long designs or motif scaffolds and expressing them to see if they fold and function. Given the model’s strengths, it seems poised to attempt de novo enzyme design or binder creation. If not already in progress, what would be the first application you’d target with La-Proteina (e.g. designing a new enzyme for a reaction by scaffolding a catalytic motif, or creating a large megadalton protein cage, etc.)? Any discussion on how well the in silico metrics correlate with experimental success (perhaps referencing prior work) would help set expectations for readers interested in deploying these designs.\n\n\nIf the authors address the weaknesses outlined above, or provide a right justification for the points raised in my questions, or clarify points I may have misunderstood, I would be willing to raise my score from 8 to 10.", "limitations": "", "rating": 8, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- The proposed representation elegantly addresses a core difficulty in protein generation: the mixed discrete (sequence) and continuous (structure) nature with variable side-chain sizes. By encoding side-chain atoms and amino acid type into a fixed continuous latent per residue, La-Proteina avoids having to explicitly model discrete sequence choices and variable atom counts during generation. This is a novel solution not seen in prior protein diffusion models, which either treated all atoms explicitly (incurring huge complexity) or attempted fully latent approaches. The authors demonstrate that this hybrid strategy retains crucial backbone information explicitly while deferring fine atom details to a learned latent space – an approach supported by ablations (if the backbone is also put in latent, performance drops sharply). This design is well-motivated and grounded in prior successes in related domains (e.g. latent diffusions in image generation) and backbone-only protein modeling, but extends them in a non-trivial way for the joint sequence–structure task. By leveraging flow matching (a deterministic counterpart of diffusion) on this simplified space, the method can generate proteins end-to-end while maintaining high fidelity in both structure and sequence, as confirmed by the VAE’s excellent reconstruction (0.12Å all-atom RMSD, 100% sequence recovery).\n\n- State-of-the-Art Unconditional Generation Performance: La-Proteina convincingly achieves SOTA results on standard protein design metrics. On the all-atom unconditional generation benchmark (100–500 residue range), it outperforms a slate of recent models like P(all-atom), APM, PLAID, ProteinGenerator, Protpardelle and Protpardelle-1c, in nearly every metric. In particular, La-Proteina’s designs have dramatically higher co-designability (e.g. 68–75% vs ~9–37% for baselines) and designability scores, showing that its jointly generated sequences truly fold into the generated structures with high fidelity. It also produces orders-of-magnitude more diverse structures (clustering yields ~180–216 unique clusters vs tens for others) without sacrificing novelty. Importantly, structural realism is superior: La-Proteina’s samples have far better MolProbity scores than baseline outputs. Additionally, La-Proteina accurately reproduces the distribution of side-chain dihedral angles (rotamers) seen in natural protein databases. Prior methods often missed certain rotamer states or had incorrect preferences, whereas La-Proteina’s generated residues match reference distributions almost perfectly. These results support the authors’ claim of overall superior quality. The evaluation is extensive, and the improvements are significant. Notably, La-Proteina even surpasses the previous state-of-the-art “Proteina” backbone-only method on its own terms it in fact excels, presumably due to the integrated training of sequence+structure rather than sequential design.\n\n\n- A standout strength is La-Proteina’s ability to handle much larger proteins than competing methods. The paper demonstrates the generation of proteins up to 800 residues (close to the upper limit in their training set) that remain co-designable, diverse, and physically plausible. All baseline all-atom models failed catastrophically in this regime (e.g. many “collapsed” and produced no co-designable samples beyond 400–500 residues). Empirically, using the same hardware that couldn’t generate a single 600-residue sample for P(all-atom) (a 140GB GPU), La-Proteina comfortably generates 800-residue proteins. The samples are not only valid but high-quality at those lengths. It should be noted that this success is in part due to engineering choices: the authors trained on an enormous dataset of ~46 million structures (AlphaFold DB) to expose the model to long proteins.", "weaknesses": "- A notable limitation is that La-Proteina is only demonstrated on single-chain proteins, whereas many real design tasks involve multi-chain complexes or protein–protein interactions. The authors explicitly acknowledge this as future work. While focusing on monomers is reasonable for a first step (and they already handle up to 800 residues in one chain), it means the method currently cannot design binding interfaces or multi-subunit assemblies. Competing approaches have introduced multi-chain generation modes (e.g. for homomers or heteromers). Not testing La-Proteina on complexes is a missed opportunity to show generality. It is unclear how easily the model could be extended to complexes (with potentially even larger lengths), which could be challenging. The authors’ own Limitations section notes that protein assemblies and interfaces were not addressed, which are crucial for tasks like binder design. Thus, the work, while strong for monomer design, falls short on multi-chain design which remains an open challenge.\n\n- La-Proteina’s impressive performance comes at the cost of very large-scale training. The model was trained on 46 million structure-sequence pairs (essentially the entire high-quality samples of AlphaFold DB) using 128×80GB GPUs, a heavy computational load. This far exceeds the training dataset sizes of most baselines (many prior models used on the order of 0.1–1 million PDB-derived examples). While the ability to leverage massive data is a plus for performance, it raises concerns of reproducibility and fairness of comparison. Some of La-Proteina’s gains might come from sheer dataset scale and network size, rather than purely algorithmic superiority. It’s plausible that if others had similar GPU budgets or training data, the gap might narrow. The authors do mention that P(all-atom) and others are constrained by architecture from scaling to AF2 data, which justifies their approach. However, from a practical standpoint, not all researchers can train on tens of millions of samples. The paper would be stronger if it discussed how performance scales with data (e.g. is a subset of 1M or 10M sufficient to beat baselines?). Is it because of the new architecture or simply training on an unprecedented dataset?\n\n- As with most computational design papers, this work stops at in silico metrics. A natural question is whether La-Proteina’s designs are actually foldable and functional in vitro. The paper does not include any experimental assay or even Rosetta energy minimization analysis to check stability. While such validation is beyond the scope of ICLR, it means the ultimate utility is inferred rather than proven. For example, co-designability uses ESMFold (a fast structure predictor) to verify that the sequence can fold into the model’s structure. This is a reasonable proxy, but ESMFold is not as accurate as AlphaFold2 on novel sequences; some false positives/negatives could occur. The model might generate sequences that fool ESMFold but would not truly fold (or vice versa). Also, MolProbity scores being good is encouraging, yet those are still computed on the designed models themselves. Without relaxation or physics-based evaluation, we don’t know if slight clashes would resolve or if the designs have hidden strain. Functionally, the motif scaffolding examples are promising (they preserved active-site geometries), but the paper doesn’t test if the enzymes would actually be active, that would require molecular dynamics or lab experiments. Again, this is not expected in a CS-focused venue, but it’s a gap to be aware of. One could imagine that certain subtleties (like global stability or kinetic foldability) are not captured by the metrics used. This is a general weakness of the field rather than this paper specifically, but since the authors tout “fully atomistic high-quality structures,” an expert might ask for a bit more evidence (e.g. computing Rosetta folding stability or sequence conservation analysis). The paper does perform a rotamer analysis and secondary structure content check, which are good sanity checks. However, one missing evaluation I note is any measure of thermodynamic stability or model confidence for the generated proteins. For example, methods like AlphaFold2 or Rosetta Relax could be used on the designed sequence to see if it strongly prefers the designed structure. Co-designability partly does this (AlphaFold via ESMFold), but reporting an average pLDDT could add insight. In summary, the lack of real-world validation is a weakness insofar as the paper’s claims rest on proxy metrics. This is not a fatal flaw for an ML paper, but it means the true impact (e.g. designing a new enzyme from scratch) is still unproven.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "j5LyNq9bKd", "reviewer": "Reviewer_gg8b", "summary": "This paper introduces **La-Proteina**, a generative model for the joint design of full-atom protein structures and their sequences.\n\nThe key innovation is a **partially latent representation**:\n*   The protein backbone is modeled explicitly in 3D space.\n*   The sequence and side-chain atoms are captured in fixed-size latent variables.\n\nUsing flow matching on this representation, La-Proteina models the joint distribution of sequence and structure. The authors report that their model achieves state-of-the-art performance on co-designability and structural validity, surpasses previous methods in motif scaffolding, and uniquely scales to generate proteins up to 800 residues long.", "questions": "1.  **On the Choice of Training Data (AFDB vs. PDB):** The model was trained exclusively on the AlphaFold Database (AFDB), which consists of predicted structures. Could the authors elaborate on the rationale for not incorporating high-resolution experimental structures from the Protein Data Bank (PDB), which are often considered the gold standard by the structural biology community? What is the authors' perspective on the potential impact of using computationally \"distilled\" data from AFDB versus empirical data from PDB on the model's learned distribution and its generalization to real-world design tasks?\n\n2.  **On the Performance of a Fully Latent Representation:** It is a very interesting result from the ablation study that a fully latent representation (the CA-enc. variant) leads to a significant degradation in performance. Do the authors have a deeper analysis or intuition for this phenomenon? In the generation trajectories of other state-of-the-art models (e.g., Pall-Atom, AlphaFold 3), it is often observed that the backbone structure emerges from the noise before the side-chains are fully resolved, even when the model architecture treats them jointly. Does the failure of the fully latent variant in this work suggest a fundamental difficulty in coupling the degrees of freedom for both backbone and side-chains into a single, unified latent space? \n\n3.  **On Modeling Long-Range Side-Chain Interactions:** *Figure 8* suggests that the VAE's latent representation for side-chains is predominantly local. Given that long-range interactions between side-chains are critical for protein folding, stability, and function, how does the proposed partial-latent modeling framework ensure these non-local dependencies are captured? Unlike methods that explicitly model all atoms in a global context, it is not immediately clear how this is achieved here. Are there specific case studies or quantitative metrics that can demonstrate the model's ability to generate plausible long-range side-chain interaction networks?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.  **Innovative Representation for Full-Atom Generation:** The paper proposes a novel partially latent representation for full-atom protein design. By modeling the backbone explicitly while encoding sequence and side-chain information into a fixed-size latent space, the method effectively addresses the long-standing challenge of variable side-chain dimensionality. The application of flow matching to this hybrid representation is a sound and well-motivated approach for modeling the joint distribution.\n\n2.  **Strong Empirical Performance on Key Benchmarks:** The model demonstrates strong performance across a range of challenging tasks. The results indicate state-of-the-art capabilities in both unconditional generation and various motif scaffolding scenarios. A particularly notable result is the model's ability to generate viable proteins up to 800 residues, demonstrating a level of scalability and robustness that surpasses many existing baselines.\n\n3.  **Thorough and Informative Ablation Studies:** The inclusion of extensive ablation studies is a commendable aspect of this work. The authors systematically evaluate the impact of different design choices related to the model architecture, training process, and sampling strategy. This analysis not only supports the paper's conclusions but also provides useful insights for researchers in the field.", "weaknesses": "1.  **Lack of Analysis on Generated Sequence Properties:** For a model that jointly generates full-atom structures and sequences, a notable omission is the characterization of the generated sequence distribution. Prior work in both inverse folding and all-atom generation has shown that models can exhibit significant biases, often over-representing certain amino acids (e.g., Alanine, Glutamate) compared to natural distributions. It is unclear if La-Proteina suffers from a similar sequence bias. An analysis of the amino acid frequencies and other sequence-level properties would be crucial for a complete evaluation of the model's capabilities.\n\n2.  **Potential Confounding Factors in Comparative Evaluation:** The experimental setup in *Table 1* may not provide a fully controlled comparison. La-Proteina was trained on proteins up to 500/800 residues, whereas the baselines were trained on significantly shorter sequences (e.g., APM < 384, Pall-Atom < 128). Evaluating all models on lengths between 100-500 residues means that La-Proteina is largely operating in-distribution, while the baselines are forced to generalize out-of-distribution. This introduces a significant confounding variable (the training data scale and distribution), making it difficult to isolate the true performance benefits of the proposed latent diffusion approach itself. A more compelling comparison would involve evaluating La-Proteina when trained on a dataset of a similar scale to the common baselines.\n\n3.  **Incompleteness in Key Evaluation Metrics:**  While this paper relies on an RMSD threshold for success, other models like APM and Pall-Atom incorporate an additional pLDDT score criterion to ensure that the refolded structures are not only accurate but also predicted with high confidence. The omission of pLDDT analysis is a concern. Could the authors report the distribution of pLDDT scores for the successfully refolded designs?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)