Ambient Proteins - Training Diffusion Models on Noisy Structures
Authors: Giannis Daras
Jeffrey Ouyang-Zhang
Krithika Ravishankar
Constantinos Costis Daskalakis
Adam Klivans
Daniel Jesus Diaz
Venue: NeurIPS 2025 spotlight ()
Keywords: ambient
diffusion
protein
de novo protein design
Primary area: machine_learning_for_sciences
TL;DR: Training protein generative model with noisy synthetic structures

Abstract: We present Ambient Protein Diffusion, a framework for training protein diffusion models that generates structures with unprecedented diversity and quality. State-of-the-art generative models are trained on computationally derived structures from AlphaFold2 (AF), as experimentally determined structures are relatively scarce. The resulting models are therefore limited by the quality of synthetic datasets.  Since the accuracy of AF predictions degrades with increasing protein length and complexity, de novo generation of long, complex proteins remains challenging. Ambient Protein Diffusion overcomes this problem by treating low-confidence AF structures as corrupted data.  Rather than simply filtering out low-quality AF structures, our method adjusts the diffusion objective for each structure based on its corruption level, allowing the model to learn from both high and low quality structures. Empirically, ambient protein diffusion yields major improvements: on proteins with 700 residues, diversity increases from 45% to 85% from the previous state-of-the-art, and designability improves from 70% to 88%.

Ambient Proteins: Training Diffusion Models on Low Quality Structures
Giannis Daras CSAIL, MIT gdaras@mit.. edu
Jeffrey Ouyang-Zhang Computer Science, UT Austin
Krithika Ravishankar Computer Science, UT Austin krithravi@utexas. edu
jozhang@utexas.co edu
Costis Daskalakis CSAIL, MIT costis@csail mit. edu
Adam Klivans
Daniel J. Diaz Computer Science, UT Austin danny. diaz@utexas edu
Computer Science, UT Austin kl klivans@cs.c utexas... cttrsiccs.teeasssee edu
Abstract
We present Ambient Protein Diffuusin, a framework for training protein diffusion models that generates structures with unprecedented diversity and quality. State- of-the-art generative models are trained on computationally derived structures from AlphaFold2 (AF), experimentally determined structures relatively scarce. The resulting models are therefore limited by the quality synthetic datasets. Since the accuracy of AF predictions degrades with increasing protein length and complexity, de novo generation of long, complex proteins remains challenging. Ambient Protein Diffusion overcomes this problem by treating low- confidence AF structures as corrupted data. Rather than simply filtering out low-quality AF structures, our method adjusts the diffusion objective for each structure based on its corruption level, allowing the model to learn from both high and low quality structures. Empirically, Ambient Protein Diffusion yields major improvements:
proteins with 700 residues, diversity increases from 45% to 86% from the previous state-of-the-- and designability improves from 68% 86%. All of our code, models and datasets are available under the following repository: http://ggtttb.ooommoma//////nanp
1 Introduction
Proteins are the fundamental building blocks of life. They accelerate chemical reactions by many orders of magnitude, convert sunlight into food, and underpin the myriads of processes within cells and organisms with the level of accuracy and precision required to sustain life 66 32]. Unlike computational protein engincering-wii which focuses improving the developability function of existing proteins through computationally guided mutations for practical biotcchnological applica- tions [21 40
52 dee protein design aims create entirely proteins with specified structures and functions, ultimately seeking to discover folds and activities not found in na- ture 22 Since protein function is largely determined by tertiary and quaternary structure, generative machine learning frameworks for protein design focus on learning the sparse, evolutionarily sampled landscape of protein structures. with the goal of generating novel, functional backbone scaffolds
24 41
36
20
beyond those observed in nature [50] 33 34 28
23 53 22 55 47]
Recent breakthroughs in machine lcarning-basee structure prediction-men notably Al- phaFold2 229] have made possible to infer accurate protein structures directly from se-
"qqual contribution.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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This progress has enabled the creation of large-scale structural resources such as the AlphaFold Database (AFDB), which contains over 214M predicted structures from UniProtKB sequences 13 46 In parallel, high-throughput tools for sequence and structure compar- ison, such as MMSeqs2 and FoldSeek, have facilitated the curation of large, diverse training datasets from AFDB [.. Among them, the 2.3M AFDB cluster dataset, has already been shown to improve the capabilities of generative models for protein structure design [34]] 23
quence (29 II 35
The quality of generative model depends on the size and fidelity of its training data. While AlphaFold2 (AF) has enabled large-scale protein structure prediction, its outputs often contain biological or computational inaccuracies [31]. To estimate the reliability of predicted structure, AlphaFold provides a per-residue confidence score, the predicted Local Distance Difference Test (pLDDT), which is proxy of local structural accuracy. In practice, researchers frequently filter predicted structures based on average pLDDD scores, training only on high-confidence subsets (typically using cutoff of pLDDT 80). However, lower PLDDDT scores are disproportionately associated with longer and more structurally complex proteins. As a result, filtering based on pL.DTT introduces bias toward smaller, simpler folds, reducing structural diversity in the training set and impairing the model's ability to generalize to more complex regions of structure space-including longer proteins. Notably, many low-pLDDT structures still contain well-folded domains that are misoriented with respect to each other, as reflected by low predicted alignment error (pAE). These structures can still offer valuable domain-leved and coarse- coarse-grained information about the structure distribution, which discarded by overly aggressive filtering.
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Figure Long protein generation performance. We train Ambient Protein Diffusion on proteins up to 768 residues and sample sequences ranging from 300 to 800 residues. Our 17M parameters model significantly outperforms the previous state-of-the-art Proteina [23], which is 200M parameters model. Ambient Protein Diffusion generates both diverse and designable structures across all lengths.
To mitigate these issues, we depart from the standard paradigm of aggressive filtering of low- confidence structures. Instead, we introduce Ambient Protein Diffusion -a framework for training diffusion models that incorporates proteins with noisy incomplete structures directly into the training process. Ambient Protein Diffusion builds on recent advances in learning generative models
from corrupted data [14 [6
15
42
49
17
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27], which have explored controlled
1 and masking [15] Our framework generalizes these techniques to arbitrary, unknown corruption processes, enabling the training of generative models in scientific domains where the corruption mechanism is complex and non- parametric. In our setting, the AlphaFold prediction errors represent such a corruption: they are structured, not explicitly modeled, and vary across protein size and topology. Yet, our method effectively leverages these imperfect samples to significantly advance the capabilities of generative protein models. For example, on proteins with 700 residues, our 16.7M parameter model improves diversity from 45% 86% and increases designability from 68% to 86% compared the previous state-of-the-art, Proteína 23 200M parameter model. Below, we summarize our key contributions:
corruption settings such as additive Gaussian noise 14
16
We generalize recent approaches for training generative models on corrupted data to handle arbitrary, non-paramen paramereeeric, and unknown corruption processes, enabling their application to scientific domains.

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Used during training
eLDOT>80
80-pLDDT-30
PLDOT-80
Not used during training
t=
4
Noising Process
Figure 2: Overview of Ambient Protein Diffusion AlphaFold structures. Rows 1-3 show the noising process (from left to the right) of three different AlphaFold proteins based on their average pLDDDT (top: high, middle: medium, and bottom: low). These proteins only used during training at the green diffusion times. At these noise levels, any initial AlphaFold prediction errors in low-pLDDT proteins have effectively been "crased" by the added noise, and the distributions of low- and high proteins have merged.
We demonstrate that framework, Ambient Protein Diffusion, effectively leverages low- PLDDT AlphaFold predictions, allowing the model to learn from all available samples without distorting the underlying structure distribution.
We further construct new training set from the AFDB cluster dataset optimized for geometric diversity irrespective their evolutionary relationship, yielding a broader and more representative sampling of structural space for generative modeling.
We achieve state-of-the of-toe-atttt-ee art results in both diversity and designability for protein generation, improve diversity by 45% and designability by 24% on long proteins (800 residues), and establish the Pareto frontier between these objectives on short proteins (< 256 residues). Our models also achieve oftte-of-the-art novelty scores both short and long protein generation, indicating much lower memorization of the training set.
2 Background and Related Work
De novo Protein Generation. Most de novo protein generation frameworks that operate in structure space follow a three-step pipeline: (1) a generative model samples a three-dimensional backbone structure; (2) an inverse folding model (e.g.. ProteinMPNN (19] proposes amino acid sequences likely to fold into the generated backbone; and (3) these sequences are evaluated by a structure prediction model (e.g.. ESMFold (35) identify the ones that best recapitulate the target fold.
Pioncering methods such as RFDiffusion [50] and Chroma 28 have established strong basclines for backbone generation. More recent advances include Genie 33 which introduces a denoising diffusion model with an SEuuieqqivvarint network that generates proteins as point clouds of reference frames; Genie2 34] which scales Genie using synthetic AlphaFold structures improve training data diversity; and Proteína (23), which replaces diffusion with flow matching and scales both model size and dataset scale by orders of magnitude to improve performance on longer and more complex monomeric proteins.
Ambient Protein Diffusion is built using the Genie architecture and makes use of ambient protein diffusion to achieve sfate-of-hhe-add art results with substantially shorter training times, much fewer parameters (16.7M vs 200M), and significantly reduced computational requirements.
Training Datasets. Recent advances structure prediction- notably AlphaFold2 [2] and ESMFold (35] hhae dramatically expanded the available structural data, enabling the prediction

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of ~214 and ~61M monomeric protein structures from UniProtKB (via the AlphaFold Protein Structure Database) 46 and metagenomic libraries (via the ESM Atlas) [3 respectively. While this explosion of computational structures presents unprecedented opportunities, it also poses significant challenges for downstream bioinformatic analysis and model training. particularly due to the scale, redundancy, and uneven quality of the predicted structures. To address this, prior work applied MMSeqs2 [26] and FoldSeek [45] to cluster the AlphaFold Database (AFDB), yielding ~2.3 clusters shown to capture evolutionary relationships between predicted structures [S]. This AFDB cluster dataset has since served as the foundational dataset to train several generative protein structure
models 23 34).
In this work, we apply a reparameterized FoldSeek the AFDB cluster dataset to maximize geometric diversity rather than evolutionary insights. Our goal is to construct a dataset better suited for learning a generative model of protein structure space- one that emphasizes structural rather than evolutionary variation. Starting from the 2.3 million AFDB clusters, we use the cluster representatives with average PLDDT > 70 (~1.299M structures) and apply our geometric clustering procedure. The resulting dataset comprises roughly ~292K structurally diverse clusters.
Diffusion Models. The goal in diffusion modeling is to sample from an unknown density Po that we have samples available. Formally, let D { ) a dataset of N independent samples, where Xá ~ Po. The unknown distribution po is potentially complex, high-dimensional and multimodal. To make the sampling problem more tractable, in diffusion modeling we target smoothened densities pr defined as the convolution with a Gaussian: pt - Po * (0, o² (t) where (I) is an increasing function of t, with o (0)- O. In particular, the object of interest in diffusion modeling is the score- function of the smoothened densities, defined as 2,, log Pc The latter is connected to the optimal
denoiser (in the l2 sense) through Tweedie's Formula: V log pr (zz) = X
o²(
Given access to E[Xo|X, xx one can sample from the distribution po of interest by running a discretized version of a reverse diffusion process 3
10 Hence, the sampling problem
becomes equivalent the problem of approximating the set of functions [E[Xo]XX, = +)) Given
a sufficiently rich family of functions {hg : 6 E θ), the conditional expectation at a particular time t can be learned by minimizing the objective:
J(0) (o, Beo. [[lho((z)) zo
In the context of protein diffusion models for backbones, Xo captures the 3-D co-ordinates for each residues of the protein.
Learning from noisy data. Recent work has explored the problem of learning diffusion models from corrupted data. Typically, the corruption process is simple, e.g. can be additive Gaussian noise in [14] II. masking in [ ( Even in works where the corruption process is more general, the degradation needs to be known and multiple diffusion trainings are required until an Expectation- Adpectation-Maxiiizaat Maximization algorithm converges 42 In this work, we deviate from this setting as the corruption process is unknown and complex, which may include AlphaFold learning and hallucination errors, and noise inherent to the structural biology technique used to solve the structure, etc. We also target a single diffusion training instead of performing multiple EM iterations. The method is detailed in Section 3
for the additive Gaussian noise case. Particularly, in [16, the authors consider learning from dataset D = { 4) of samples noised with additive Gaussian noise of different variances (o² -- Formally, let X Xo (tt)
Our work generalizes the techniques developed in 14 16
where Xo ~ Po, Z ~ NO0 Ia). Each point X,, contributes to the learning only for t 2 t, using the objective:
j(0) [EE
Σ
E Ees (e [[oo(t
(1 ac(t(4)))xe - N., [P]
(2)
2e, ED: 124,
att, t.) o0(0) As the number of samples grows to infinity, Equation 2 also recovers the
conditional expectation E[.o|X, = xx), but it does so while being able to utilize noisy samples.
2 AAltennttvv formulations of diffusion modeling, such as the Variance Preserving case, are equivalent to this case up to simple reparametrization, For the ease of analysis, we focus our presentation on corruptions of the form X, Xo + a,L, Z ~ (O,

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This objective recovers the true minimizer because one can prove that the conditional expectation E|X,, Xx zel. lies in the line that connects the current noisy point z; and the prediction of the clean image, [ X mt)-
Distribution merging under noise. A key idea in our method will be that distribution distances contract as we increase the noise level added. In the context of diffusion models, this property has been leveraged in the SDEdit (39 paper to allow diffusion models to perform atroke-based editing at inference time without any finetuning. Most relevant to our work, Ambient Omni [18] uses the distribution contraction property (together with other innovations) to use blurry and out-o--distribution data during training. In this work, we focus on synthetic data from AlphaFold that arise from various corruption sources: biological ones (errors in the crystallography process), computational ones (errors in the solution of the inverse problem from the crystallography data to the modeled structure), and learning ones (AlphaFold mistakes due to the limited size of the training dataset and hallucinations).
3 Method
3.1
Building Intuition
We are given access to samples from the AlphaFold distribution Po and aim to learn how to sample from the true distribution of experimentally solved structures, Po, without an explicit degradation model mapping Po Po. Our key insight is that, regardless of how Po deviates from po. adding noise to both distributions causes them to contract toward one another. As the noise level increases, the distributions P.. and pt become progressively more aligned. This is because it is known that Gaussian noise contracts distribution distances (KL divergence) in the following sense:
DKL (pelle) s (Pe || pe), v2
In fact, as é oo, we have that: (PL pe) + 0, as both distributions converge the same Gaussian. We now define the concept of merging of two distributions towards the same measure.
Definition 3.1 (e-merged) We say that two distributions, p and p are e-merged, if the KI. distance between the two is upper-bounded, by e, i.e., D |I () S c.
Similarly, we define the merging time of two distributions the minimal amount of noise we need to add such that the two distributions become e-merged. Formally,
Definition 3.2 (c-merging time) Let distributtion p. P. We define their e-merging time as follows: (. = inf(t: (K x (10, (0)) 11 (O. I)) S <c).
Assuming we can estimate the c-merging time between two distributions p and p. our key idea is to treat samples from 6r approximate samples from p: for all timesteps t t, (p. p, c). This idea is illustrated in Figure 2 The intuition is that once the distributions have sufficiently merged under noise, the residual shift becomes negligible and samples from ýt can be used for learning Pt. This holds because: (i) the learning algorithm may not be sensitive to small distributional discrepancies at high noise levels, and (ii) even if some bias is introduced, the remaining diffusion trajectory for times t < tx (p. P. E) is robust to small initial distributional mismatch due to its inherent stochasticity. For more in depth analysis of the mathematics behind this intuitive idea we refer the reader to the work of Daras et al. [18].
Sample dependent noise levels. At high level, our objective is determine the e-merging time between the distribution of proteins. key challenge arises from the fact that the AlphaFold distribution highly heterogeneous in structural fidelity- that is, the accuracy with which AlphaFold predicts the true protein structure varies widely across samples. is well established that short, structurally simple proteins are predicted with higher confidence, while longer and more complex proteins tend to yield lower-confidence predictions. This trend is illustrated in Figure (Left). If we were to assign a single noise level across the entire AlphaFold dataset, we would need to select a relatively high noise level to accommodate the lowest-confidence predictions, particularly from long proteins. This would unnecessarily degrade the training signal for high-confidence structures regardless of protein length-and limit the model's
structures and that of experimentally resolved
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ability to learn from clean supervision. To address this, we treat the AlphaFold dataset as a mixture of K uub-distributions, 91 92...... ... each representing a distinct confidence regime. We then assign each sub-distribution an appropriate noise level, sufficient to bring it e-close to the distribution of high-confidence structures under the same noise schedule. This formulation allows the model to effectively learn from high-confidence AlphaFold predictions and incorporate low-confidence structures in a controlled manner, mitigating the degradation typically caused by noisy training data.
A natural way to decompose the Alphafold distribution into a mixture of quality-specific sub- distributions is to leverage AlphaFold's self-reported confidence metric-the average predicted Local Distance Difference Test (pLDDT) score as proxy for predicted structural fidelity. In particular, given dataset D {(>16) pLDDT( Ji= () a hyperparameter to be chosen) with empirical observations for the j-th distribution being all the (j)
consider K distributions (where K is
samples ((=6) PLDDT(") c - PLDDT(") < c for some hyperparameters e Cmaxx
Choice of sub sub-distribution boundaries. In this work, we adopt a deliberately simple and conservative strategy by partitioning the AlphaFold dataset into three discrete quality regimes based on the average PLDDT score: high-quality proteins (pLDDT > 90), medium-qualit proteins (pLDDT in [80, 90) and low-quality proteins (pL.DTT in [70, 80)). We acknowledge that this discretization is coarse and that more principled alternatives may yield further improvements- for instance, by optimizing the bin boundaries or learning continuous mapping from pLDDT diffusion time. Despite the simplicity of our choices, our experimental results demonstrate that even a naive quality-aware decomposition can lead important gains in performance across both short and long proteins. It is important to emphasize that there are two sources of benefit over filtering methods: 1) low-quality data (previously discarded) increases diversity, and 2) the distinction we do between medium-quality and high-quality data boosts designability. The population of proteins that have pLDDT lower than 70 has a very high merging time, and we did not see significant benefits from including them. To improve training efficiency and save computational resources, we decided to discard this subpopulation. We underline that training algorithms that are adaptive to local corruption (rather than global, i.e. average pLDDDT) might be able to benefit from such proteins we leave this direction for future work.
3.2 Ambient Protein Diffusion Algorithm
Our algorithm takes as input a dataset of protein structures together with their average PLDDT score, D = [(xg0) (6) ()DDT(() _ a diffusion schedule, (t), and a mapping function f [o, 100] + R+ that translates the average PLDDT value of protein to its estimated e-merging time.
Annotation stage. The first step of the algorithm replaces each protein in the dataset with a noisy version of itself, where the noise level is determined by the mapping function f. This function is a hyperparameter for our algorithm- in our experiments, we opt for a rather simple choice (sce Appendix Table 16 for full deseription of our training configuration), but in principle this can be an arbitrary function defined by the user based on their specific domain knowledge or experimental findings. After this transformation, each protein can be treated as sample from the target distribution convolved with a Gaussian at its assigned noise level. This transformation step is only performed once during dataset preprocessing, i.e., we replace the low-quality protein with noisy version of itself before we start the training. This is important because adding different noise realizations across epochs can lead to recovery of the original low-quality protein if the noise is averaged out.
Loss function. After the annotation stage, we need to solve a training problem where we have data corrupted at different noise levels with additive Gaussian noise, as in 14 [6]. Hence, we can use the objective of Equation?? 2 Instead of directly applying the loss, we first need to rescale each time t to account for the vanishing gradient effect that due to the multiplicative factor a(t). Specifically,
we need to rescale the loss at time / with: w=((= क. (o=())-'"())))" such that we balance the
a a1())
different timesteps. This weighting is derived following the methodology of the EDM [30 paper (Appendix, p. 26, Section B6). We underline that this rescaling was not mentioned in the original paper of Daras et al. [16 14,, for training with noisy data. Yet, we find this rescaling critical for the success of our method. We hypothesize that the authors of [14 16] did not encounter this issue because there were at most two noise levels considered, while in AF predicted protein structures there is whole spectrum of assigned noise levels based on the predicted quality (measured by average

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Dannleed
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Protein Length Datribution
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Reclustering the AFDB cluster dataset to improve generative protein modeling. (A) Starting from the 2.3M AFDB clustered dataset, cluster the representatives with FoldSeek optimized for geometric similarity: alignment-type set to TM-Align, TM threshold set to 0.5. and coverage set to 0.75. This results in a 300K clusters (pLDDT 70) from which we keep the representatives for training. (B) PLDDTT and protein length statistics for our new training set. (C) Overlay of two Ambient clusters: Top row: Representative (beige; UniProt A0A2W1EPGI) overlaid with members A0A820X4G2 (left, red) and A0A446YZW1 (right, red). Bottom row: Representative (cyan; UniProt A0A395XDB6) overlaid with members A0A3BOYRI6 (left, blue) and LOS475 (right, blue). In the original AFDB cluster dataset, each of these six proteins was designated as the representative of its own cluster despite their similarities in structural features.
Figure 3:
PLDDT) of protein structure. We provide further details about the loss implementation in the Appendix (Section E and pseudocode in Algorithm T
Uniform Protein Sampling in terms of diffusion times. To perform a training update for diffusion model. we typically sample point from the training distribution and then we uniformly sample the noise level f. However, since in our case we are dealing with noisy data, not all times t are allowed for given protein, i.e. protein with (LDDT( is only used for times 2 ((PLDDT()). To avoid spending most of the training updates on very noisy proteins, we opt for sampling first the diffusion time and then select from the eligible proteins that can be used in that diffusion time. This strategy ensures balanced coverage across the diffusion trajectory from low to high noise-whilee still leveraging the diversity of low-confidence structures (pLDDT 80) in training dataset.
Our algorithm requires three simple changes to the regular diffusion training: 1) an annotation stage (before training) where each low-quality protein is replaced with noisy version of itself, 2) a change in the way we fetch samples from the dataset so that we do not overallocate training updates to highly noisy proteins and 3) change in the loss function to account for the fact that for some proteins we do not have access to an uncorrupted structures.
Summarizing:
3.3 Reclustering AFDB clusters for generative modeling applications
On top of our algorithmic contributions, we also reconsider the choices made for the training dataset. The AFDB clustered dataset (5) has been used to train several generative protein models [34, (3).. However, the original intent behind the clustering was to study structure evolution. Thus, the hyperparameters were chosen to obtain clusters of homologous structures, and the authors report that 97.4% of pairwise comparisons within clusters are conserved at the H-group (Homology) level of the ECOD hierarchical domain classification (median TM-score 0.71). While these FoldSeek hyperparameters are well-suited for evolutionary analysis, we found that the AFDB cluster dataset has a significant degree of structural duplication and near-duplication between clusters that are more distantly evolutionarily related (see Figure 3P. This structural redundancy leads to an imbalanced training set, where structural motifs from the larger protein superfamilies are overrepresented.
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Given this finding, we hypothesize that the datasets for generative modeling of protein struc- tures parsscuaalllllly for backbone-bused models- benefit more from clusters defined purely by geometric similarity. To that end, we construct new clustering dataset derived from the AFDB cluster representatives, with an exclusive focus on structural topology. Specifically, these are the changes we made to the FoldSeek hyperparameters: we switch the alignment-type from 3Di+AA to TM-Align to improve fidelity, we use a TM-score threshold of 0.5, and we relax the alignment coverage from 0.9 to 0.75, We did the latter to improve clustering of AlphaFolded proteins with extended, unfolded N- or C-terminal regions (i.e., noodle tails) (Figure(3C) This approach produced a more balanced dataset that samples structural folds more uniformly, independent of their evolutionary relationships. Ablations that disentangle the contribution of this reclustering from our ambient training approach are given in Figure 4
Experimental Results
We build on the Genie2 codebase [34]. Our model architecture follows the Genie2 architecture except that it is scaled larger, using 8 triangle layers opposed to 5. We train Ambient Protein Diffusion in 3 stages with increasingly longer proteins, eventually reaching proteins up to length 768. For details on the training process, Appendix Section E.3 and for details on metric,s
Appendix Section D We underline that the computational cost of training our model is relatively low compared to the prior state of the Proteína model. This is due the decreased size of our model (< 17M vs 200M) and training set (~ 290K vs ~ 780K). We further note that our goal is to develop models that perform well across range of tasks, including long-protein generation, motif scaffolding, and more. To this end, we train only two models for the purposes of this paper: one model optimized for long-protein generation (Figure I and another optimized for short-protein generation (Figure
4.1 Comparisons on unconditional generation of longer proteins
In Figure we compare Ambient Protein Diffusion performance on generating backbone for proteins with length ranging from 300 to 800 residues. To directly compare with Proteína on long- long-protein generation, we adopt its three-stage training and evaluation protocol. During training, the maximum sequence length is capped at 768 residues. For evaluation, we sample 100 protein backbones at each target length and evaluate them using the designability and diversity metrics. Since Ambient Protein Diffusion builds on Genie2, we use the same sampling a noise scale of 7 = 0.6. This noise scale parameter controls the trade-off between the designability and diversity by reducing the amount of stochasticity added in the reverse process, as it is typically done in the protein generative modeling literature (see Appendix E.4.1 for details).
-rnnndure--unninggg 1000 diffusion steps with
Ambient Protein Diffusion achieves designability and diversity scores exceeding 90% for proteins between 300 and 500 residues, and maintains scores above 85% for lengths up to 700 residues. For 800-residue proteins, both metrics decline to 68%. Compared to Proteína, Ambient Protein Diffusion outperforms by 26% in designability and 91% in diversity length 700, and by 24% and 45%, respectively. at length 800. At every protein length, Ambient Protein Diffusion's 's diversity is equal to its designability, indicating that every designable protein is unique, This is not the case for Proteína, where diversity scores consistently fall below designability, regardless of protein length.
Taken together, these results demonstrate the impact of ambient diffusion on backbone-based genera- tive models and highlight the strength of Genie2's s equivariant architecture. Our 17M parameter model trained on approximately 290K AlphaFold structures significantly outperforms a 200M-parameter transformer model trained on roughly 780K proteins. Our results show that smaller, more efficient models can surpass larger transformer baselines in both structural diversity and designability.
4.2 Ablating the significance of Ambient Diffusson
In comparison to Genie2, the starting point of our implementation, we made the following changes: 1) made the model bigger, 2) trained on longer proteins, 3) reclustered the dataset to optimize for geometric similarity rather than evolutionary similarity, and 4) used low PLDDT AlphaFold proteins as noisy data using our Ambient Protein Diffusion framework. To quantify how much of the improvement comes from the latter step, we train an Improved Genie2 without the Ambient Framework for training with corrupted data and report results in Figure 4 We find that while
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Figure 4: Ablation to quantify the effect of the Ambient Protein Diffusion framework. We improve upon Genie2 by making the architecture bigger, reclustering the dataset in Scction 3.3 and by finetuning on longer proteins (up to 768 aminoacids). The resulting improved Genie2, shown in Orange, outperforms Genic2 but still lags behind our Ambient Protein Diffusion Model, shown in blue. The only difference between the two models is that Ambient Protein Diffusion uses low PLDDT AlphaFold structures as noisy data, as explained in Section 3.2 Ambient Protein Diffusion consistently outperforms both the improved Genie2 baseline and Genie2, with increasingly significant improvements sequence length grows.
our two models perform similarly on proteins 300 residues, the designability and diversity of baseline diminish longer proteins. For proteins with 800 residues, the number of designable clusters drops from 68% to 25%. Ambient Protein Diffusion shows a marked improvement, maintaining a stable number of designable clusters. We underline that the difference comes solely from the training algorithm since the architecture, model size, hyperparameters, and inference algorithm remain the same. We note that this experiment only ablates the impact of treating AlphaFold data noisy, and fixes the reclustered dataset (Section 3.3 for both models. We examine the impact of reclustering separately in Section
B.3 and find that reclustering increases diversity; however, without Ambient training, the designability remains low. Both innovations are needed to achieve optimal results.
4.3 Comparisons on unconditional generation of shorter proteins
In this experiment, evaluate the model the unconditional generation of shorter proteins in 5 We provide training details for the model optimized for short protein generation in the Appendix Section E.3.2
Divensiy Dentgrabi
Following the Genie2 protocol, we generate 5 structures for each se- quence length from 50 to 256 residues, yielding total of 1,035 structures. The generated structures are evaluated for both designability and diversity. In line with prior work, we sweep the noise scale 7y to explore the trade- off between designability and diver- sity. Ambient Protein Diffusion out- performs previous methods on both metrics, establishing new Pareto frontier that achieves superior perfor- mance compared all existing mod- els, including Proteina.
Jonte
Siverity
Figure Designability- diversity trade-off for short protein generation (up to 256 residues). Ambient dominates completely the Pareto frontier between designability and diversity, while using 12.88x smaller model. We further do without using any higher-order sampler or (auto-) guidance method.
4.4
Novelty scores
The next step show that our method does not just memorize proteins, but instead it can generate novel designable structures that are distinct from the training set. Here, we compute the TM-novelty metric following the protocol of Geffner reproducing the literature TM-novelty scores, which we discuss in detail in Appendix Section D.3
(23]. However, we found two key issues when
First, since Spring 2025 FoldSeek resolved bug computing the alntmscore (Github issue 312). which makes all previous reported values incorrect. Second, found that Geffner et al. 23

---

Table 1: PDB and AFDB TM-Novelty for short protein generation. For each model, we sample 5 structures for each sequence length from 50 256 residues, yielding a total of 1,035 structures. lower TM-Novelty score is better.
Model
PDB Novelty ())
AFDB Novelty (L)
Ambient Proteins
0.35
0.774
0.848
? 0.55
0.773
0,851
= 0.65
0.774
0.858
Baselines
Genie2
0.789
0.862
RFDiffusion
0.853
0.923
Proteus
0.842
0.884
Chroma
0.824
0.885
Proteina (FS 7 = 0.35)
0.853
0,910
Proteina (FS 7 0.45)
0.837
0.898
Proteina (FS 7 = 0.5)
0.831
0.893
Proteina (FS no-tri 7 0.45)
0.832
0,891
Proteina (21M 7 = 0.3)
0.889
0.932
Proteina (21M 7 0.6)
0.854
0.905
inadvertently used the TM-TM-Sc from the row with the highest qTM-Score, rather than from the row with the highest aln To ensure accurate benchmarking with the literature, recalculated TM-Novelty with the patched FoldSeek v10 for several baselines, explicitly selecting the max aln alnTM-Scone for each query. We report results in Table I For backward compatibility, reproduced literature results using the unpatched FoldSeck v9 and the default qTM-Scor sorting (Table 15). Moving forward, we strongly recommend that adopting FoldSeek v10 and always using the max aln'T---n---- TM-Scree value to determine the novelty per query when computing I'M-Novelty.
also
Using both versions of FoldSeek, Ambient Protein Diffusion sets new state-of-the-art TM-novelty scores on both the PDB and AFDB (588K) benchmarks. In the short-evaluation regime (S 256 AAs) using FoldSeek v v10, we exceed the next-best model (Genie2) by 2.0% on PDB and 1.6% on AFDB-despite Genie2's restriction to proteins no longer than 256 AAs. Against Proteina, we further boost TM-novelty by 7.0% PDB and 4.8% on AFDB. In the long- longeevaluation regime (300-800 800 AAs). we focus on comparison with Proteina. Here, we achieve TM-novelty scores of 0.682 on PDB and 0.740 AFDB, representing improvements of 18.4% and 16.2%, respectively. Together, these results demonstrate that Ambient Protein Diffusion, driven by the Ambient loss and cluster dataset, produces the most novel proteins across both short and long-sequence settings.
4.5 Motif Scaffolding
As final evaluation, we compare our method prior work in motif scaffolding. The full results are shown in Appendix Figure 7 and in Appendix Tables II and 12 With y 0.45, Ambient Protein Diffusion generates 1.923 unique successful scaffolds for single-motif tasks, a significant improvement over Genie2's ' 1,4 1,445 34] and performs comparably to a Proteína model (2,094 (23). which is much larger (200M parameters vs 17M parameters) and is optimized specifically for motif scaffolding. For multi-moti scaffolding, Ambient Protein Diffusion generates 89 unique successful structures across of the 6 problems, outperforming Genie2, which produces 40 and solves 4.
5 Conclusion
We introduced Ambient Protein Diffusion, a framework for protein structure generation that leverages low-confidence AlphaFold structures source of noisy training data. Ambient Protein Diffusion enables the generation of long protein structures with unprecedented levels of designability. diversity and novelty. Diversity increases as it can use low-confidence Alphafold structures that are typically discarded and designability increases as we separate the pristine quality proteins structures from the medium quality A FphaFoold predictions. Ambient Protein Diffusion represents a foundational step toward robust de novo protein design at more natural, biologically relevant lengths.
10

---

6
Acknowledgements
This research has been supported by NSF Awards CCF- 19F-1991292, ONR grants 400014-25-1-21 16, N00014-25-1-2226, a Simons Investigator Award, and the Simons Collaboration on the Theory of Algorithmic Fairness. The experiments were run on the Vista GPU Cluster through the Center for Generative AI (CGAI) and the Texas Advanced Computing Center (TACC) UT Austin.
Note on authorship. William Daspit and Qiang Liu joined the team after an initial version of this project submitted to NeurIPS. Both authors made major contributions to the final version. Due to the NeurlPS policy preventing authorship changes after submission, their names could not appear the paper the conference website. However, all the authors of this manuscript agree that they made very significant contributions and that this project would not be the same without their work. A version of this paper with the updated authorlist is available bioarXiv:
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NeurIPS Paper Checklist
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2. Limitations
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A Limitations and Future Work
This work represents a first step toward protein generative models that make better use of the synthetic structures from the AlphaFold Database. Nevertheless, there are several clear avenues for improve- ment. (i) Structure-qualic metric. We rely on AlphaFold's self-reported pLDDT score-a coarse, residue-averaged confidence measure that can itself be noisy or misleading. (ii) Data coverage. We only use one representative per AFDB cluster rather than incorporating all available cluster members, and we build on the existing AFDB clustering rather than reclustering the full 114M-structur dataset, (iii) PLDDT-merging -erging--tiim -imme mapping. Our choice of how to translate pLDDT values into merging thresholds was driven by empirical tuning rather than by a systematic ablation study or principled selection criterion, (iv) Experimental validation. Ultimately, the real test of any generative model is whether its predictions hold up in the laboratory. We have yet to confirm our structures experimentally.
B
Ablations
B.1 Mapping function ablations
The algorithm described Section 3.2 assumes a mapping function that maps a protein's 's pLDDT to a diffusion time after which the protein can be used for learning. For all the experiments of the paper, we used a discrete map (detailed in Table To) in particular proteins that have pLDDT 2 90 are used everywhere, proteins with PL.DTT in 180, 90) are used for only the last 400 diffusion steps (out of the 1000 total) and proteins that have PLDDTT [70, 80) are only used for the last 100 diffusion steps. This mapping was chosen to represent three coarse categories; clean samples, semi-clean proteins and very noisy AlphaFold predictions. In this section, we ablate the choice the mapping function to I) show the robustness of our method to reasonable choices, and 2) show that it is possible to achieve improved results by optimizing this mapping.
We show results in Table 2 for small changes to the default choice used in the paper. Specifically, we change what happens when we inflate deflate all the PLDDT boundaries in the discrete chosen mapping by 5 PLDDT points and we observe the differences in designability and diversity. For all these results, we use noise scale y = 0.6 during sampling. As shown, our method is relatively robust, as small perturbations to the mapping don't 't lead to very substantial change. In fact, the inflated thresholds lead to model that belongs to the Pareto frontier of Figure 4 in the paper. Running the same model with y 0.65 leads to another Pareto point, achieving an (86.6, 0.882) designabiliy--diveriiy pair.
plddt_ to timestep
Designability
Diversity
Notes
(80,0)
95.2
0.590
Genie2 baseline
98.6
0.781
Paper choice
(75,3))) (55.0),85.300)),555.9)
96.4
0.780
Deflated thresholds by
96.8
0.783
Inflated thresholds by 5
Table 2: Effect of changing the PL.DDT-to-timesee function. Slight adjustments to the thresholds
lead to reasonable results, indicating that the method is robust.
Now that we established the robustness of our approach, we present further results that can be obtained by optimizing the PLDDT to timestep mapping. Towards that goal, we try using more discrete bins and we also explore two continuous generalizations interpolate between the PLDDT boundaries used in the paper. In particular, we try a piecewise continuous function and a sigmoid function. To explain with example, before all proteins with PLDDT in (80, 90] were used for times 300-1000. Under the piecewise continuous generalization, protein with pLDDT in (80, 90] will be used for times >= 300- (90- 2)/(90 80), e.g. a protein with pLDDT 82 is used for times t >= 240. The results are given in Table
As shown, by optimizing the mapping function, we can even outperform the results we obtained in the paper. That said, even simplistic choice, as the ones we opted for the paper, can already yield significant boosts over the Genie2 baseline.
17

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pLDDT to timestep mapping
Designability
Diversity
Pareto
Notes
98.6
0.781
Pareto optimal
Paper choice
Piecewise linear
96.2
0.827
Pareto optimal
Sigmoid
98.2
0.752
95.9
0.742
Extra bins Extra bins 2
94.2
0.858
v Pareto optimal
Table 3: Effect of different DLDD'T-to-tmesste mappings. Several mappings achieve Pareto optimality, balancing designability and diversity.
B.2 Weighting function ablation
In the paper, used the weighting term w(t) = -00
(f))))) in the Ambient loss to
o e1())
a=(t)
balance the contribution of different diffusion times and avoid vanishing gradients. We ablate this choice in Table 4 As shown, removing that weighting leads to significant deterioration of the obtained performance, both in designability and diversity. The calculations for this weighting follow the EDM 30 methodology, Appendix p. 26, Section B6.
Weighting
Designability 98.6
Diversity
Pareto
Paper choice Constant (w=1)
0.781
v Pareto optimal
97.4
0.733
Table 4: Effect of weighting term w(t) (t²(1)- (t,)))
o (1())
in the loss.
B.3 Dataset reclustering ablation
In Figure 4 of the main paper, we fix the dataset to the geometric reclustered version we created in this work, and we ablate the effect of Ambient training. In this section, we perform additional experiments to understand the standalone value of geometrie reclustering. We report results with all recluresting in Table As shown
combinations of Ambient vs. Ambient and reclustering in the Table, reclustering leads to improved diversity, but without Ambient designability is low. Both innovations are needed to achieve the optimal performance.
Setting
Dataset
Designability + Diversity 1
No Ambient
Genie2
95.2
0.590
No Ambient
Re-clustered
81.4
0.902
Ambient Genie2
96.4
0.501
Ambient Re-clustered
98.6
0.781
Table 5: Effect of dataset reclustering. Re-clustering increases diversity, but without Ambient training. the designability low. The combination of the two innovations yields the optimal results.
B.4 Loss ablation
For low PLDDT structures, zo cannot be trusted. Instead, our loss involves predicting a noisy version of the low pLDDT protein, which can be trusted more than the original protein because, intuitively, the noise has erased some the AlphaFold prediction mistakes. For completeness and to support argument, provide further ablation where train model with the same setup as the srort-protein generation the paper, but using 2o prediction loss instead of the proposed loss. Results shown in Table
For more detailed discussion on the benefits of the Ambient loss over the original diffusion loss, we refer the reader to the work of Shah et al. 43
18

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STA (5
Figure 6: Additional qualitative visualizations of unconditional generations.
19

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Loss Type Ambient loss
Designability
Diversity
98.6
0.781
To prediction loss
98.5
0.753
Table 6: Effect of Ambient loss. Ambient loss achieves slightly higher designability and diversity compared to zo prediction loss.
Single Motif Scaffolding Performance
Multimotif Scaffolding Performance
Number of Unique successes
Number of Unique Successes
(Out structures)
Genie 2
(Out of 1000 structures)
Genie Ambient
3FDiffusion Proteina Ambient
10
10
10a
10a
6E6R Jong
6EX2 Jong
GEBR, med
17CR
STRV Jero
6EXZ meed
THRX 120
6E6A stort
STRY STRV_me m_emee
30XT
STAN
7MRX 60
1Q/G
STRV stort
SYU:
42YP
1PAW
SIUS
18C1
5WNV
24L8
381K+-8095 3895
1PRW four
1PRW TWO
GEXZ
Figure 7: Performance on Motif Scaffolding Tasks. We compare Ambient Protein Diffusion to state-of-the-art models for motif scaffolding. The graphs show the number of unique successful scaffolds generated for each single- and multi-motif task. No model produced successful scaffolds for 4JHW and 3NTN. Only Ambient Protein Diffusion produced a valid solution for multi-motif' scaffolding of 2B5I.
C Additional Results
C.1 Motif Scaffolding Results
We additionally compare our method to prior work on motif scaffolding in Figure 7 with full results provided in the supplement. Our evaluation follows the Genie2 benchmark, which comprises 24 single-motif and 6 multi-motif design tasks [34 50). For each task. generate 1,000 scaffold samples using a noise scale of 7 = 0.45. A design is considered successful it (1) satisfies Genie2's motif designability criteria and (2) preserves the motif with an RMSD below 1Å. Among successful designs, scaffold is counts unique if its TM-score is at most 0.6 when compared to any other successful scaffold. task is considered solved least one successful scaffold is generated.
With = 0.45, Ambient Protein Diffusion generates 1,923 unique successful scaffolds for single- motif tasks, a significant improvement over Genic2's 1.445 (34) and performs comparably Proteína model (2,094 (23]) that is much larger (200M parameters vs 17M parameters) and is optimized specifically for motif scaffolding. Notably, all methods solve similar number of motifs RFDiffusion solves 22 of the 24 tasks, while Ambient Protein Diffusion, Genie2, and Proteína each solve the same tasks. For multi-motic scaffolding, Ambient Protein Diffusion generates 89 unique successful structures across 5 of the 6 benchmark problems, outperforming Genie2, which produces 40 and solves Ambient Protein Diffusion performs particularly well on the 1PRW W_four motif (38 vs. 11 successful structures) in which scaffold is generated surrounding calcium binding motif [48). Overall, Ambient Protein Diffusion outperforms existing methods such as Genie2 and RFDiffusion single-mout motif tasks and matches the performance of Proteína model optimized specifically for scafo--caafolddng.
We want to underline that when counting successes in motif scaffolding it is important to fix the scaffold length for given motif for all the baselines. In particular, we noticed that increasing the protein length leads to consistent improvements. For fair comparison between models, we provide results for Ambient Protein Diffusion, Genie, and RFDiffusion, where increasing the scaffold lengths by 1.5 increased the total number of successes. Assuming we use the midpoint of the mininum and maximum scaffold lengths as provided in the Genie benchmark (structures are provided by the RFDiffusion benchmark. but the lengths are from Genie), Genie generates 1327 successes, Ambient
20

---

Protein Diffusion generates 1849, and RFDiffusion generates 694. If we increase the length by 1.5, Genie, Ambient Protein Diffusion and RFDiffusion generate 2486, 3776 and 1033 successful scaffolds respectively.
C.2 Secondary Structure Evaluations
In this section, we systematically evaluate the Secondary Structure Proportions of our generated proteins. Specifically, we first use biotite to assign secondary structure labels to all the generated proteins. Then, look the designable PDB files, we calculate the percentages of alpha/beta/loops. and then we average those over all designable PDBs. The results are shown in Table 7
Method Genie2
a-Helix (%) 1
3-Sheet ( (%)
72.7
4.8
Proteina MFS 0.35
71.6
5.8
Proteina MFS 0.45
68.1
6.9
Proteina MFS 0.50
67.0
7.2
Ambient Protein Diffusion (scale 0.5)
69.9
7.9
Ambient Protein Diffusion (scale 0.4)
66.6
9.5
Table 7: Secondary structure composition across methods. Lower a- c-Helix and higher B-Sheet percentages indicate more natural outputs.
As shown, Ambient Protein Diffusion generates proteins with more beta sheets and loops compared to Proteina and Genie2, illustrating progress towards designing more natural proteins. That said, all the models, including ours, show bias towards alpha helices. One way mitigate this bias is through secondary structure conditioning. In our code, we further release a model that can be conditioned on a per-residue SS label. As increase the Classifier Free Guidance strength towards beta sheets, this model generates proteins with more interesting SS structure, as summarized in Table Preliminary designability/diversit evaluations show weaker performance of this model compared to the unconditional models of our main paper. Optimally balancing structural diversity and strong designability/diversity metries remains a challenging open problem.
Guidance strength
a- a-Helix (%) 4 3-Sheet (%)
0.2
82.1
1.5
0.4
61.8
11.4
0.6
30.3
33.6
0.7
21.7
36.1
Table Effect of guidance strength on secondary structure composition. Increasing the strength reduces a- e--Hlix content and increases B-Sheet content, indicating shift towards more natural
outputs.
C.3
Complete Tabular Results
This section presents the full numerical tables corresponding result figures shown in the text. Specifically,
Table
enumerates the results in Figure and Figure
Table 10
enumerate the results in Figure
Table
enumerates partial results in Figure 7
Table 12
enumerates partial results in Figure
21

---

Table 9: Long protein generation performance. Best values per residue length highlighted in bold. Ambient Proteins results are shown for y = 0.6. Found in main text Figure
Residue Length
Model
Designability (%)
Diversity (Clusters)
Ambient
90
89
Proteina
93
55
300
Proteus
93
23
Improved Genie2
93
93
Genie2
81
80
Ambient
92
92
Proteina
85
60
400
Protcus
83
35
Improved Genie2
79
79
Genie2
60
60
Ambient
91
91
Proteina
82
65
500
Proteus
30
Improved Genie2
71
71
Genie2
20
20
Ambient
87
87
Proteina
81
55
600
Proteus Improved Genie2
67
20
51
51
Genie2
3
Ambient
86
Proteina
68
45
700
Proteus Improved Genie2
47
10
30
30
Genie2
0
Ambient
68
68
Proteina
47
800
Proteus
5
Improved Genie2
25
25
Genie2
0
Table 10: Designability-diverity trade-off for short protein generation. Designability and diversity for short protein generation. Found in main text in Figure
Model
Designability (%t)
Diversity (t)
Ambient Proteins
? 0.35
99.2
0.615
0.55
98.6
0.781
7 0.65
93.0
0.867
Baselines Genie2
95.2
0.59
FoldFlow (base)
96.6
0.20
FoldFlow (stoc.)
97.0
0.25
FoldFlow (OT)
97.2
0.37
FrameFlow
88.6
0.53
RFDiffusion
94.4
0.46
Proteus
94.2
0.22
Proteina (FS 7 = 0.35)
98.2
0.49
Proteina (FS 7 0.45)
96.4
0,63
Proteina (FS 0.5)
91.4
0.71
Proteina (FS no-tri 7 0.45)
93.8
0,62
Proteina (21M 0.3)
99.0
0.30
Proteina (21M 7 0.6)
84.6
0.59
Proteina (LoRA = 0.5)
96.6
0.43
22

---

Table 11: Performance Single Motif Scaffolding Tasks Ambient Protein Diffusion achieves superior results to Genie 2 and RFDiffusion and performs on par with Proteina. Crucially, our model achieves these results zero-shot, i.c., unlike Proteina, it is not optimized for motif scaffolding and still achieves comparable performance while being an order of magnitude smaller. Found in text in Figure 7
Motif Name
Genie 2
RFDiffusion
Proteína
Ambient Protein Diffusion
6E6R long
415
381
713
601
6EXZ Jong
326
167
290
432
6E6R med
272
151
417
406
1YCR
134
7
249
146
STRV long
97
23
179
119
6EXZ med
54
25
43
69
7RRX 128
51
44
6E6R <ho__hhort
26
23
56
27
STRV_med
23
22
23
7MRX 85
23
13
31
17
3XX
3
8
4
STPN
8
5
4
11
7MRX_6
5
1
QJG
5
3
5
STRV short
3
3
SYUI
3
5
4
4ZYP
3
6
11
3
6EXZ_shon
2
3
3
IRWW
1
1
1
STUS
1
1
1
1
IBCF
1
1
1
1
5WN9
0
2
2KL8
1
1
1
1
4JHW
0
0
Total
1445
889
2094
1923
Table 12: Performance on Multi Motif Scaffolding Tasks Ambient Protein Diffusion achieves consistently superior results to the predecessor Genie-2 model, despite using the same architecture, iee. the benefit comes from better use of the data. The motif 2B5T only solved by Ambient Protein Diffusion. Found in text in Figure 7
Motif Name
Genie 2
Ambient Protein Diffusion
3BIK+3BP5
17
23
IPRW four
11
38
1PRW two
8
15
45WN
12
2B5I
0
1
3NTN
0
0
Total
40
89
23

---

Table 13: Performance Comparison Single Motif Scaffolding Tasks with Constant Midpoint
Length
Motif Name
Genie2
Ambient
RFDiffusion
Lengths
6E6R_lon
406
601
208
108
6EXZ_lom
296
432
158
110
6E6R_ _ed
286
406
70
78
1YCR
78
95
70
STRV long
85
119
40
116
6EXZ med
46
69
17
80
7MRX 128
28
44
52
128
6E6 short
25
27
48
STRV med
33
23
9
86
7MRX 85
24
17
12
85
3XXT
5
62
5TPN
2
62
7RRX _R
1
1
60
QQG
2
2
103
78
STRV short
2
4
56
SYUI
2
1
75
4ZYP
2
2
40
6EX S/oort
50
IRWW
82
SIUS
1
1
99
IBCF
124
5WN9
1
42
2KL8
79
4JHW
0
0
0
75
Total
1327
1849
694
D Evaluation Metrics
Evaluation of a protein generative model is challenging and there have been few metrics that have been proposed. In what follows, explain standard metrics in the protein-generative modeling literature that we will use in our Experimental Results section. Our experiments report using Proteína's definitions of the metrics when possible.
D.1 Designability
Designability (also referred to refoldability) assesses the structural plausibility of generated proteins. Given a generated backbone, ProteinMPNN [19] generates eight plausible amino acid sequences for that backbone. ESMFold then folds each sequence and the resulting eight structures are compared to the original backbone. The self-consistency RMSD (scRMSD) is defined as the smallest root mean squared deviation between the generated backbone and each of the eight refolded structures. A backbone is considered designable if scRMSD < 2 Á and designability is defined as percentage generated backbones that meet this criterion.
D.2 Diversity
Diversity quantifies the structural variability among the generated proteins. Designable backbones are clustered using Foldseek with a TM-score threshold of 0.5. Diversity is then defined as:
Number of Designable Clusters
Diversity = Number of Designable Samples
This metric reflects the proportion of structurally distinct (i.e., non-redundant) designable backbones among all designable samples.
24

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Table 14: Performance Comparison on Single Motif Scaffolding Tasks with 1.5x Length
Motif Name
Genie2
Ambient
RFDiffusion
Lengths
6E6R 6EnR_onn
439
720
243
162
6EXZ long
526
848
193
165
6E6R med
393
633
117
1YCR
321
459
25
105
STRV long
64
102
14
174
6EXZ_ _md
349
490
19
120
7MRX_12 128
14
23
192
66 short
145
215
72
STRV_m
82
109
5
129
7MRX 85
23
42
15
127
3XT
48
27
93
STPN
16
40
13
93
7RX 60
9
10
2
90
QJG
323
117
STRV short
11
10
2
84
SYUI
112
4ZPP
6
13
60
6XZ EXZ_short
31
75
IRWW
1
123
SIUS
149
IBCF
186
5WN9
63
2KL8
1
1
118
4JHW
112
Total
2486
3776
1033
Table 15: PDB and AFDB TM-Novelty for short protein generation using FoldSeck-v9 and max qTM-score row. We recompute all values using Geffner et al. [X]] method. Numbers reported by Geffner et al. [23] are shown in parenthesis. These numbers are reported for backwards comparisons only and strongly encourage the community to use the corrected TM-Novelty scores reported in the main text (see Appendix D.3).
Model
PDB Novelty (L)
AFDB Novelty (L)
Ambient Proteins
7 0.35
0.604
0.663
7 0.55
0.606
0.671
7 0.65
0.608
0.673
Baselines
Genie2
0.621 (0.63)
0.685 (0.69)
RFDiffusion
0.711 (0.71)
0.779 (0.77)
Proteus
0.741 (0.74)
0.766 (0.76)
Chroma
0.686 (0.69)
0.732 (0.74)
Proteina (FS 7 0.35)
0.727 (0.71)
0.783 (0.77)
Proteina (FS 7 = 0.45)
0.709 (0.69)
0.769 (0.75)
Proteina (FS 7 0.5)
0.698 (0.69)
0.760 (0.75)
Proteina (FS fs__nottr--
0.45)
0.702 (0.69)
0.759 (0.76)
Proteina (21M 7 0.3)
0.811 (0.81)
0.841 (0.84)
Proteina (21M =0.6)
0.761 (0.72)
0.797 (0.77)
25

---

D.3 Novelty
Metric definition. Novelty is a metric that assesses the uniqueness of the generated backbones in comparison to existing structures in database. We compute the novelty score with respect both AFDB and PDB datasets following Geffner et al. [23]. To compute novelty, we measure the structural similarity of each designable protein to those in the dataset using FoldSeek's easy-search command used by Proteina:
foldseek easy-search <path_sample sample> <database_pathl <out_file> -alignment-type 1 -exhaustive-searde -tmscore-threshor 0.0 -max-seqs 10000000000 -format-output query, target, alntmscore, 1ddt
For each designable backbone, we keep the max alntmscore value rather than the alntmscore value of the first row, which is the max gimscore value. The novelty of the dataset is the average of these maximum alntmscore values, representing how distinct our generated structures are from the proteins in the reference database (i.e., do df. groupby ("query") [" ""alntmscore"]] .max () mean ()). Perhaps counterintuitively. high novelty is not desired since it implies high similarity to the existing database.
Bug in novelty computation. Several of our evaluation metrics TM--iversity and TM-Novelty- depend on FoldSeek's TM-score implementation. In Fall 2024, however, FoldSeek developers identified a bug in the alntmscore output (see Github issue 312 titled "aintmscore output is wrong" for details), which means that all previously reported T'M-based metries in the literature that did not use FoldSeek v10 (release 10-941cd33) are incorrect. Additionally, we found that Geffner et al. (23) mistakenly computed TM-novelty by taking the aln'TM-Score from the row with the highest TM-Score, rather than from the row with the highest alnTM-Score. This oversight arises because Foldseek's easy-searchs command, by default, sorts its output in descending order by qTM- Score-inrespectivee of the requested output format.
To ensure accurate and comparable benchmarking with the literature, we recalculated TM-Novelty with the patched FoldSeek v10 (release 10-941cd33), explicitly selecting the maximum aln Score for each query. For backward compatibility, also reproduced literature results using the unpatched FoldSeek v9 (release 9-427df8a) and the default max q qTMMScore row. Moving forward, we strongly recommend that the community adopt FoldSeek v10 and always sort using the alnTM-Sccre output to determine the maximum TM-Score per query and correctly compute TM-Novelty. Using both versions of FoldSeek, Ambient Protein Diffusion sets new offte-of-the-art TM-novelty scores on both the PDB and AFDB (588K) benchmarks.
E Full Training Algorithm and Implementation Details
E.1
Additional Implentation Details
Loss buffer. The loss rescaling introduced in the main paper ensures balanced weighting across noise levels. At the same time, it also introduces potential instability: the loss explodes (I) approaches (t.). To mitigate this instability, we define buffer zone around each protein's 's assigned noise level. Specifically, given a protein's 's assigned noise level f;, is only used during training at timesteps t T,, where 7 is a buffer hyperparameter that controls the exclusion margin. This constraint prevents the model from encountering degenerate gradient behavior near the rescaling boundaries and is only applied to medium and low confidence structures (pLDDT < 90). We underline that is similar to how in normal diffusion there buffer time zone around t 0 that is never sampled.
Ambient in high-noise regime. As explained in the main paper, each protein is only used for a subset of diffusion times according its average PLDDT value. The proteins that have super high PLDDT (> 90) are considered clean data and can be used with the normal training objective. However, as found in 43, using the Ambient training objective for high-noise might be useful even if clean data is available. Intuitively, this objective prevents memorization and promotes diversity in the outputs. We ablated this design choice, and we found a slight increase in diversity for the same designability by using this. Hence, used this tool from 43 for all our Ambient Protein Diffusion trainings.
26

---

E.2 Algorithm
We provide the full algorithm in Algorithm T We commit to open- open-iou our code and models to facilitate the broader adoption of our method from the community.
Algorithm Ambient Protein Diffusion: Training Algorithm.
Require:
(t) (LDDD(())))) ) PLDDT to diffusion time untrained network has dataset D = [(ag] mapping function f : [0, 100] + RT, noise scheduling (t),, batch size B, diffusion time T, buffer
{(x!)) )) (pLDDT())) (<x) pLDDT(") e ~ (NO
1: D
Noise each point the training set according to its pLDDT and get (noisy, noise level) pairs.
2: while not converged do
(B) f- Sample uniformly times in [0, / >> Sample diffusion times for this batch. Dp - (Duffle(D)
3:
ts
4:
Shuffle dataset. Initialize loss. b Initialize index at shuffled dataset.
5:
loss
6:
pos <-
7:
for i [1, B] do
8:
while True do
>> find the first eligible point
9:
by - D [pos]
10:
t 2 t + then
11:
break
12:
else
13:
pos pos
Move the next point in the dataset.
14:
end if
end while
16:
~~ 1),
>> Sample noise.
t (1)
D. Time be used in this training update. D- Assigned time based on the PLDDT value Noised point the assigned time. Add additional noise.
18:
ti + ty
Nt, t y
20:
84 & It;
(1)
(t)-
alt, t4)
o²())
22:
w(t, (4) x (r(())-a'(())))-
D Loss reweighting.
23:
loss loss + w(t, (4) (l + a(t, ((t,t))))= s.,
Ambient loss
24:
end for
25:
loss loss
Compute average loss.
B + 0 - V gloss
26:
b Update network parameters via backpropagation.
27:
end while
E,3
Model and Training Hyperparameters
E.3.1
Hyperparameters for model optimized for long generation.
We train Ambient Protein Diffusion in 3 stages with increasingly longer proteins. the first stage, we train on proteins from 50 to 256 residues for 200 epochs our ambient clusters dataset using the representatives (~ 196,000 proteins). Since we increased the batch size to 384 items, we adopted learning rate schedule improve convergence (25). We train with the AdamW optimizer with maximal learning rate of 1.0 x 10-4, During the second and third stage, we include additional cluster representatives of at most 512 and 712 residues, which scales our dataset to ~269,000 and ~291,000 1,000 proteins respectively. Training is performed on 48 GH200 GPUs and runs in 18, 48, and 48 hours for each stage respectively. We underline that the computational cost of training significant, is still relatively low compared to the Proteina's estimated 14 days training on 128 100 GPUs. This is due the decreased size of our model (< 17M 200M) and training set (~ 290K vs ~ 780K).
model, while
Table 16 includes more thorough list of the hyperparameters used for experiments.
27

---

Table 16: Hyperparameters of the diffusion protein model. Dashes (-) indicate that the value the same as the previous column. The Ambient walls correspond to the assigned diffusion times based on the protein's s pLDDT (times are from to 1000). Proteins with pLDDT > 90 are used everywhere. Proteins with pLDDT > 80 are used for times in [600, 1000] and proteins with pLDDT > 70 are used for times in [900, 1000]. We underline that these hyperparameters were not particularly optimized, and even more benefits might be observed by properly tuning these values.
Hyperparameter
Genie2
Ambient (Stage 1)
Stage 2
Stage
Diffuusion
Number of timesteps
1,000 Cosine
Noise schedule
[1, 1000). pLDDT 2 90 [600, 1000], 90 pLDDT 2 80
Allowed times:
[900, 1000]. 80 pLDDT 2
Model Architecture
Single feature dimension
384
Pair feature dimension
128
Pair transform layers
8
Triangle dropout
0.25
Structure layers
8
Training
Optimizer
AdamW
Number of training proteins
586k
196k
269k
291k
Number epochs
40
200
50
20
Warmup iterations
10,000
1,000
500
100
Total batch size
384
384
96
48
Learning rate
1.0 10-4
1.0 x 10
1.0
10
1.0
10
Weight decay
0.05
Minimum protein length
20
50
50
Maximum protein length
256
256
512
768
Minimum mean PLDDT
80
70
70
70
Compute Resources
Number of GPUs
48
48
48
48
Training time
18 hr
18hr
48hr
48hr
28

---

E.3.2 Hyperparameters for model optimized for short generation.
The Ambient Protein Diffusion model used in this experiment was trained on dataset filtered with TM-Align threshold of 0.4 (as opposed 0.5), resulting in a training set of approximately 90K cluster representative proteins. While it is well known that protein pairs with TM-scores above 0.5 typically share the same fold, and those below 0.5 generally do not, we find that the trade-off between designability and diversity is sensitive to the underlying structural heterogeneity of the dataset. Notably, clustering with a TM-align threshold 0.4, which corresponds to less than 1 chance of shared global topology, slightly outperforms the 0.5 threshold, which reflects ~38% probability of topological similarity [54].
E.4 Sampling
E.4.1
Noise scale
In diffusion modeling, one designs forward Ito corruption process:
dX, = s(Xx, O)d + g())dB,,
(4)
defined by the drift function f(-..) and the noise coefficient g()). This process gets initialized at distribution po and diffuses over time, defining smoother densities pe. Due to remarkable result by Anderson 3 sampling from po achieved by running the reverse process:
+ g t log Pr + g(T t)dBr- (5)
initialized pr-
However, in the context of protein generative models, it has been observed that sampling from discretized version of the reverse process of Equation O does not lead to good performance as measured by the available metrics. Hence, common practice the protein generative modeling literature to sample from tilted measure using the process:
dX (-f(rr--f(T - + t) log + +( - (tdF-r (6)
where the parameter 7y controls the stochasticity added to the generation. Typically, this parameter set to values < 1 leading to more designable proteins the expense of reduced diversity in the generated samples. The goal is often to optimally control the trade-off between designability and diversity, i.c. to be able to produce wide range of structurally and functionally diverse proteins. Unless stated otherwise, for the experiments this paper, we use 7 = 0.6 (as done in Genie2 334
E.4.2 Hyperparameters and sampling methods
1000 sampling steps using a simple first-order discretization of Equation ( We underline that results could be further enhanced by using more advanced sampling techniques such autoguidance [1] (used in Proteina (23)), higher-orde samplers (30] and test-time scaling (38) methods.
For sampling, we follow the exact same parameters as Genie2. In particular,
29


Reviews:
[{"review_id": "88QP6HcTFE", "reviewer": "Reviewer_6ytr", "summary": "The paper proposes Ambient Protein Diffusion, which trains diffusion models on noisy AlphaFold structures by adjusting the objective based on corruption levels, avoiding filtering low-pLDDT data. It reclusters AFDB for geometric diversity, boosting diversity to 85% and designability to 88% for 700-residue proteins, outperforming prior work with a 16.7M-parameter model. This advances de novo protein design for complex lengths by leveraging both high and low-quality structures.", "questions": "- The spirit of the ambient diffusion is to utilize low quality data where only timesteps t>ti are taken into consideration. I am not sure whether first construciting the (x(t(i)), t(i)) paris is necessraty. Since you can just first sample a data point, and sample t according to its plddt. In this way, you do not need to change the loss funciton (parameteerized by x(t(i)), and using the original loss function (h(xt) - x0) is enough. I think they are mathematically equvilant. Correct my if I am misunderstanding the approach. \n- In line 318, did you remove the low-quality data?", "limitations": "NA", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "## Strengths\n\n- This study fully leverages low-pLDDT AlphaFold structures by treating them as “corrupted” data, a novel approach in protein design that avoids discarding valuable low-confidence structures and instead adjusts diffusion objectives based on corruption levels.\n- The method achieves SOTA performance on long proteins (up to 700 residues), boosting diversity from 45% to 85% and designability from 70% to 88% compared to prior methods, with a significantly smaller model (16.7M parameters).  \n- This study constructs a new training dataset by reclustering AFDB for geometric diversity (not jsut evolutionary similarity), yielding structurally diverse clusters that better represent protein structure space for generative modeling.\n\n\n\n## Weaknesses\n\n- Limited ablation studies on some key parameters. \n  - How does the mapping function (f) (line 202) influence the results?\n  - Can you present diffirent choices of the weighting factor w(t) (line 215)?\n- Unclear contribution attribution: No systematic ablations separate the effects of the geometrically reclustered dataset from the low-pLDDT utilization method, making it difficult to determine which component drives performance gains. (besides this concern, I believe that the ambient diffusion works.)\n- The pLDDT threshold: Since you have adopted ambient diffusion, why do you filter structures with pLDDT <70 (line 294)? This potentially excludes valuable low-confidence data.\n- Model comparison: Training distinct models for short and long proteins (line 268) and comparing with single-model baselines could be a bit strange.   \n- In Figure 5, the ablation plot lacks a direct comparison with Proteína, which performs well on long proteins.", "was_revised": true, "final_justification": "My questions are fully resolved. This is a technically solid paper.", "rebuttal": "We thank the Reviewer for their time and feedback. In what follows, we present numerous ablations. We report (designability, diversity) pairs for the short-protein generation benchmark (Figure 4), as it is computationally infeasible to do long protein training for all these studies.\n\n### Mapping Function Ablations\n\n**Reviewer**: \"How does the mapping function influence the results?\"\n\n**Great question – we thank the Reviewer for raising this.**  \n\n#### Robustness\n\nIn the paper, we used the function `f` defined by the `plddt_to_timestep` mapping:\n\n(90, 0), (80, 300), (70, 900)\n\nProteins with:\n- **pLDDT > 90** are used throughout all steps (0 to 1000).  \n- **pLDDT in (80, 90]** are used from step 300 onward.  \n- **pLDDT in (70, 80]** are used only from step 900 onward.  \n\nWe will now show what happens when we slightly change the function f we used in the paper in two opposite directions.\n\n| `plddt_to_timestep` | Designability | Diversity | Notes |\n|---------------------|---------------|-----------|-------|\n| (80,0) | 95.2 | 0.590 | Genie2 baseline |\n| **(90,0),(80,300),(70,900)** | **98.6** | 0.781 | Paper choice |\n| (85,0),(75,300),(70,900) | 96.4 | 0.780 | Deflated thresholds by 5 |\n| (95,0),(85,300),(75,900) | 96.8 | **0.783** | Inflated thresholds by 5 |\n\n\nAs shown, our method is relatively robust, as small perturbations to the mapping don’t lead to a very substantial change. In fact, the inflated thresholds lead to a model that belongs to the Pareto frontier of Figure 4 in the paper. Running the same model with scale=0.65 leads to another Pareto point, achieving an (86.6, 0.882) designability-diversity pair.\n\n#### Continuous mapping functions and more bins\n\nWe further present continuous generalizations of our original choice. In the paper, we chose a very rough categorization of the proteins into “high-quality”, medium-quality, and “low-quality” for didactic purposes (L191-200). We now try:\n\ni) a piecewise linear continuous generalization.\nii) a sigmoid.\niii) more bins\n\nE.g. before all proteins with pLDDT in (80, 90] were used for times 300-1000. Under i), a protein with pLDDT x in (80, 90] will be used for times t>=300 * (90 - x) / (90 - 80), e.g. a protein with pLDDT 82 is used for times t>=240.\n\n| `plddt_to_timestep`| Designability | Diversity | Pareto         | Notes        |\n|-----------------------------|---------------|-----------|----------------|--------------|\n| (90,0),(80,300),(70,900)    | **98.6**      | 0.781     | ✅ Pareto optimal | Paper choice |\n| Piecewise linear            | 96.2          | 0.827     | ✅ Pareto optimal |              |\n| Sigmoid                     | 98.2          | 0.752     |                |              |\n| (90,0),(85,300),(80,600),(75,900),(70,950) | 95.9 | 0.742 |                | Extra bins 1 |\n| (90,0),(85,200),(80,300),(75,850),(70,900) | 94.2 | **0.858** | ✅ Pareto optimal | Extra bins 2 |\n\nAs shown, by optimizing the mapping function, we can even outperform the results we obtained in the paper. That said, even a simplistic choice, as the ones we opted for in the paper, can yield significant boosts.\n\n### Weight Ablations\n\n**Reviewer**: \"Can you present diffirent choices of the weighting factor w(t)?\"\n\nWe ablate a constant weighting function (w=1) as used in the Genie2 paper and the square root of the weighting used in the paper.\n\n| Weighting         | Designability | Diversity | Pareto         |\n|--------------------------|---------------|-----------|----------------|\n| Paper choice             | **98.6**      | 0.781     | ✅ Pareto optimal |\n| Constant (w=1)           | 97.4          | 0.733     |                |\n| Square root              | 95.0          | **0.783** |                |\n\nAs shown, the weighting we picked in the paper yields the **optimal results**. The reason this reweighting is needed is due to the factor multiplying the network prediction in the loss of Eq. (2). The reweighting we proposed corrects for this multiplication, following the derivations in the paper:  \n**Elucidating the Design Space of Diffusion Models (EDM)**  \n— *Appendix, p. 27, Section B6*.\n\nWe will detail the derivation in the Camera Ready version of our work.\n\n#### Figure 5 clarifications\n\n**Reviewer:** \"In line 318, did you remove the low-quality data?\"\n\nFigure 5 of our paper compares **three models**:\n\n1. **Original Genie2**  \n   Trained on short proteins with the original Genie2 dataset (pLDDT > 80 filtering, no reclustering).\n\n2. **Improved Genie2 (Baseline w/o Ambient)**  \n   Trained on longer proteins using the **re-clustered data, filtered at pLDDT > 70**.\n\n3. **Ambient Diffusion**  \n   Trained on longer proteins using the **re-clustered data** filtered at pLDDT > 70,  \n   *plus* the Ambient methodology for utilizing low-quality pLDDT samples.\n\nIn summary, this figure **fixes the dataset** (re-clustered, pLDDT > 70) and **ablates the Ambient methodology**.\n\n**Reviewer**: \"In Figure 5, the ablation plot lacks a direct comparison with Proteína, which performs well on long proteins.\"\n\nThe comparison (designability, diversity) is shown below:\n\n| Length | Original Genie2 | Improved Genie2 | Proteina     | Ambient Protein Diffusion |\n|--------|------------------|------------------|--------------|----------------------------|\n| L300   | (81,90)          | (93,93)          | (93,55)      | (90,89)                    |\n| L400   | (60,60)          | (79,79)          | (85,60)      | (92,92)                    |\n| L500   | (20,20)          | (71,71)          | (82,65)      | (91,91)                    |\n| L600   | (2,3)            | (51,51)          | (81,55)      | (87,87)                    |\n| L700   | (1,0)            | (30,30)          | (68,45)      | (86,86)                    |\n| L800   | (0,0)            | (25,25)          | (55,47)      | (68,68)                    |\n\nAs shown, **our Ambient Protein Diffusion model massively outperforms Proteina in long protein generation.**\n\n### More Dataset & Ambient Ablations\n\n**Reviewer**:  \"No systematic ablations separate the effects of the dataset from the low-pLDDT utilization method\"\n\nFigure 5 in the paper directly ablates the effect of using Ambient Diffusion, as it shows the effect of having it and not having it on the same exact dataset (reclustered filtered at pLDDT > 70).\n\nWe agree with the Reviewer that we need to separately ablate the need for having a re-clustered dataset. Results below:\n\n| Setting                     | Dataset              | Designability ↑ | Diversity ↑ |\n|----------------------------|----------------------|------------------|--------------|\n| No Ambient                 | Genie2      | 95.2             | 0.590        |\n| No Ambient                 | Re-clustered         | 81.4             | 0.902        |\n| Ambient                    | Genie2      | 96.4             | 0.501        |\n| Ambient                    | Re-clustered         | **98.6**         | **0.781**    |\n\n**Reclustering leads to improved diversity**.\n\n### Other clarifications\n\n**Reviewer**: \"why do you filter structures with pLDDT <70?\"\n\nIt is true that we could use proteins with lower pLDDTs too. That said, proteins with pLDDT ~70, are already used for only 10% of the diffusion training (steps from 900-1000). Hence, we don’t expect a dramatic improvement by using proteins with pLDDT<70 with our method, and we skipped those to avoid the whole AFDB dataset (estimated size ~28 terabytes).\n\n**Reviewer**: \" Training distinct models for short and long proteins [...] could be a bit strange\"\n\nThere seems to be a misconception here. Our Genie2 baseline is only trained (and optimized) for short protein generation. Proteina also uses different models to produce their short-generation and long-generation results. In fact, in Proteina there are four different models trained for short generation (Table 1 from https://arxiv.org/pdf/2503.00710). Proteina finetunes one of the four short generation models (the MFS^{no-tri}) for long generation and reports results in Figure 8 of their paper. Similarly, we fine-tune the short-protein generation model for long generation, and we report results in Figure 3 of our submission.\n\n\n**Reviewer**: \"[...] you do not need to change the loss function [...]\"\n\nExcellent question – let us clarify it here. \n\nThe Reviewer proposes predicting x0. For low pLDDT structures, x0 cannot be trusted. Instead, our loss involves predicting x_{t_n}, which can be trusted more than x0 because the noise has erased some of the AlphaFold prediction mistakes. So in terms of loss, the prediction of x_{t_n} instead of x_0 is actually critical. For completeness and to support our argument, we did one more ablation during the rebuttal where we trained a model with the same setup as the short-protein generation in the paper, but using x0 prediction loss instead of the proposed loss. Results:\n\n| Loss Type           | Designability | Diversity |\n|---------------------|----------------|-----------|\n| Ambient loss        | **98.6**       | **0.781** |\n| x₀ prediction loss  | 98.5           | 0.753     |\n\nMoving on to the Reviewer’s point about the sampling of times: is it necessary to first noise to $x_{t_n}$ and then to $x_t$ instead of noising all the way directly?\n\nThe answer is surprisingly yes (as we hint in the paper L208-209 and in our pseudocode Algorithm 1, Appendix page 6). The reason has to do with the information leakage about x0 that happens as we do multiple epochs. When the corruption to noise level x_t_n happens once, as we do in our paper, x0 cannot be fully recovered – some part of the signal has been destroyed by noise. However, if we are allowed to get multiple noise versions of it at the same noise level then we can average them out and approximately recover the signal. That’s why in a multiple epochs setting the two ways of getting x_t are not equivalent. \n\n**We believe that our rebuttal strongly addresses the Reviewer’s concerns, and we would be grateful if the Reviewer considers upgrading their score to reflect this.**"}, {"review_id": "zdVMRevegN", "reviewer": "Reviewer_zoX9", "summary": "This paper presents Ambient Protein Diffusion, a diffusion-based method for protein structure generation that incorporates low-confidence AlphaFold2 predictions rather than discarding them. The approach treats structures with lower pLDDT scores as corrupted data and adjusts the diffusion process accordingly, using per-sample noise schedules to align noisy predictions with reliable structures. Experimental results show improvements in diversity and designability compared to baselines.", "questions": "- How does the performance change as the number or boundaries of pLDDT bins are varied, or if a continuous mapping is used? Is there a principled way to optimize binning or the $f$ function?\n- Given the bias toward alpha-helical structures noted in the conclusion, have the authors examined generated structure topologies in more detail (e.g., secondary structure proportions, SCOP/CATH distribution)? What steps could mitigate this bias?", "limitations": "yes", "rating": 5, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n- The central innovation is a general framework for exploiting structures of unknown corruption by merging their distributions using a sample-adaptive noise schedule, thus integrating all available synthetic AF data without coarse filtering. This presents a flexible, data-efficient approach likely to be relevant for generative modeling in other domains with noisy scientific data.\n- Extensive experiments demonstrate strong performance in protein generation and motif scaffolding tasks, with the method outperforming state-of-the-art models in diversity and designability across most conditions.\n\n\nWeaknesses:\n- While ablation versus standard diffusion is addressed, and clustering thresholds are discussed, there is insufficient exploration of the sensitivity/robustness of the reported gains to hyperparameters, such as choice or granularity of pLDDT bins, mapping function $f$, or diffusion schedule.\n- Authors note that the method tends to generate alpha-helical structures preferentially , which remains an important unsolved limitation. This could limit the diversity of discovered proteins and undercuts one of the paper's main claims of achieving unprecedented diversity.", "was_revised": true, "final_justification": "The concerns about hyperparameters' sensitivity and generation diversity are addressed.", "rebuttal": "We thank the Reviewer for their time and thoughtful feedback. The Reviewer appreciated the novelty of our method, our strong experimental results and the potential relevance of our approach for scientific domains with noisy data. The only concerns seem to be about i) missing ablation studies about the mapping function and ii) missing secondary structure evaluation. \n\nIn what follows, we address these raised issues by:\n* providing numerous ablations about the mapping function\n* evaluating comprehensivel our secondary structure performance\n* Providing novelty numbers \n* Presenting further improved Secondary Structure results using a conditional model.\n\nFor all our ablations on the mapping function, we report (designability, diversity) pairs for the short-protein generation benchmark (Figure 4 of the paper), as it is computationally infeasible to do long protein training for all these studies.\n\n### Mapping function ablations\n\n\n#### Robustness\n\n**Reviewer:** \"there is insufficient exploration of the sensitivity/robustness\".\n\nIn the paper, we used the function `f` defined by the `plddt_to_timestep` mapping:\n\n(90, 0), (80, 300), (70, 900)\n\nProteins with:\n- **pLDDT > 90** are used throughout all steps (0 to 1000).  \n- **pLDDT in (80, 90]** are used from step 300 onward.  \n- **pLDDT in (70, 80]** are used only from step 900 onward.  \n\nWe will now show what happens when we slightly change the function f we used in the paper in two opposite directions.\n\n| `plddt_to_timestep` | Designability | Diversity | Notes |\n|---------------------|---------------|-----------|-------|\n| (80,0) | 95.2 | 0.590 | Genie2 baseline |\n| **(90,0),(80,300),(70,900)** | **98.6** | 0.781 | Paper choice |\n| (85,0),(75,300),(70,900) | 96.4 | 0.780 | Deflated thresholds by 5 |\n| (95,0),(85,300),(75,900) | 96.8 | **0.783** | Inflated thresholds by 5 |\n\n\nAs shown, our method is relatively robust, as small perturbations to the mapping don’t lead to a very substantial change. In fact, the inflated thresholds lead to a model that belongs to the Pareto frontier of Figure 4 in the paper. Running the same model with scale=0.65 leads to another Pareto point, achieving an (86.6, 0.882) designability-diversity pair.\n\n#### Continuous mapping functions and more bins\n\nWe further present continuous generalizations of our original choice. In the paper, we chose a very rough categorization of the proteins into “high-quality”, medium-quality, and “low-quality” for didactic purposes (L191-200). We now try:\n\ni) a piecewise linear continuous generalization.\nii) a sigmoid.\niii) more bins\n\nE.g. before all proteins with pLDDT in (80, 90] were used for times 300-1000. Under i), a protein with pLDDT x in (80, 90] will be used for times t>=300 * (90 - x) / (90 - 80), e.g. a protein with pLDDT 82 is used for times t>=240.\n\n| `plddt_to_timestep`| Designability | Diversity | Pareto         | Notes        |\n|-----------------------------|---------------|-----------|----------------|--------------|\n| (90,0),(80,300),(70,900)    | **98.6**      | 0.781     | ✅ Pareto optimal | Paper choice |\n| Piecewise linear            | 96.2          | 0.827     | ✅ Pareto optimal |              |\n| Sigmoid                     | 98.2          | 0.752     |                |              |\n| (90,0),(85,300),(80,600),(75,900),(70,950) | 95.9 | 0.742 |                | Extra bins 1 |\n| (90,0),(85,200),(80,300),(75,850),(70,900) | 94.2 | **0.858** | ✅ Pareto optimal | Extra bins 2 |\n\nAs shown, by optimizing the mapping function, we can even outperform the results we obtained in the paper. That said, even a simplistic choice, as the ones we opted for in the paper, can yield significant boosts.\n\n**Reviewer**: \"Is there a principled way to optimize binning or the function?\"\n\nExcellent question. Indeed, there is a principled way to find the mapping function, but implementing it might add some additional engineering steps. Essentially, the mapping function predicts the minimum amount of noise we need so that some distance (e.g., TV or KL) between the two distributions becomes less than epsilon. We can train a discriminator network to estimate this distance by seeing how much noise we need to add to confuse the discriminator. In our paper, we did not opt for this more principled solution because we were afraid it might hinder the wider adoption of the method, but we can certainly have this discussion for the Camera Ready.\n\n### Secondary Structure Evals\n\n**Reviewer**: \"have the authors examined generated structure topologies in more detail?\"\n\nFollowing the Reviewer’s recommendation, we systematically evaluate the Secondary Structure Proportions of our generated proteins. Specifically, we first use biotite (as in Proteina) to assign secondary structure labels to all the generated proteins. Then, we look at the designable PDB files, we calculate the percentages of alpha/beta/loops, and then we average those over all designable PDBs. The results are shown below:\n\n| Method                                | α-Helix (%) ↓ | β-Sheet (%) ↑ |\n|---------------------------------------|---------------|----------------|\n| Genie2                                | 72.7          | 4.8            |\n| Proteina MFS 0.35                     | 71.6          | 5.8            |\n| Proteina MFS 0.45                     | 68.1          | 6.9            |\n| Proteina MFS 0.50                     | 67.0          | 7.2            |\n| Ambient Protein Diffusion (scale 0.5) | 69.9          | 7.9            |\n| Ambient Protein Diffusion (scale 0.4) | 66.6          | **9.5**        |\n\n\nAs shown, Ambient Protein Diffusion generates proteins with more beta sheets and loops compared to Proteina and Genie2, illustrating progress towards designing more natural proteins.\n\n**Reviewer**: \"What steps could mitigate the bias towards alpha helices?\"\n\nOverall, with unconditional generation is really hard to fully capture the underlying distribution. This problem is known for image generative models too, e.g. in the recent NVIDIA paper “Guiding a diffusion model with a bad version of itself” the authors mention:\n\n“\"Furthermore, the unconditional case tends to work so poorly that the corresponding quantitative numbers are hardly ever reported. The EDM2-S model trained with ImageNet-512, for example, yields a FID of 2.56 in the class-conditional setting and 11.67 in the unconditional setting.\"” \n\nThe obvious solution is thus conditioning. Over the past two months (since the submission), we trained a model that can be conditioned on a per-residue SS label. As we increase the Classifier Free Guidance strength towards beta sheets, this model generates proteins with more interesting SS structure:\n\n| Strength Setting | α-Helix (%) ↓ | β-Sheet (%) ↑ |\n|------------------|---------------|----------------|\n| 0.2              | 82.1          | 1.5            |\n| 0.4              | 61.8          | 11.4           |\n| 0.6              | 30.3          | 33.6           |\n| 0.7              | 21.7          | **36.1**       |\n\nWe plan to make these models available together with the code release upon acceptance of our work. We will further add all the Ablations and the Secondary Structure Evaluations in the paper. \n\n**Reviewer**: \"This could limit the diversity of discovered proteins and undercuts one of the paper's main claims of achieving unprecedented diversity.\"\n\nBesides the SS evaluation results shown above, we further report novelty numbers for the models of the paper (in short and long generation) to truly show that our model can generate unique proteins:\n\n| Setting                   | Model                    | PDB Novelty ↓ | AFDB Novelty ↓ |\n|---------------------------|--------------------------|----------------|-----------------|\n| Long Protein Generation   | Ambient Protein Diffusion | **0.682**      | **0.740**       |\n|                           | Proteina                  | 0.836          | 0.883           |\n| Short Protein Generation  | Ambient Protein Diffusion | **0.774**      | **0.848**       |\n|                           | Proteina                  | 0.832          | 0.891           |\n\n**We believe that our rebuttal strongly addresses the Reviewer’s concerns, and we would be grateful if the Reviewer considers upgrading their score to reflect this.**"}, {"review_id": "zsV2p8hwkZ", "reviewer": "Reviewer_Yqh5", "summary": "Ambient Protein Diffusion (APD) tackles noisy AlphaFold2 backbones by treating each structure’s confidence score as a cue for how much Gaussian noise to inject before training; the ε-merging-time rule ensures that, after this adjustment, ambient diffusion can be applied to unknown corruption. The authors first re-cluster the AlphaFold Database by geometric similarity to create a 292 k-structure, fold-diverse dataset, then fine-tune a 17 M-parameter Genie-style network for less than five days on 48 GH200 GPUs. Despite its modest size and compute budget, the resulting model surpasses the much larger 200 M-parameter Proteína on backbone designability and diversity up to 700 amino acids, beats vanilla diffusion baselines on short-protein tasks, and produces more novel motif scaffolds. Overall, APD shows that embracing low-confidence structural predictions—not discarding them—can broaden protein-space coverage and deliver state-of-the-art generation efficiency.", "questions": "- Provide a short formal derivation (or appendix) of the ambient loss starting from the ϵ-merging definition.\n- Add ablations for:\n    1. alternative *f*(pLDDT) mappings (e.g., linear, sigmoid, more bins);\n    2. re-clustering + standard training vs. original clustering + ambient training.\n- Quantify secondary-structure composition—e.g., helix/strand/loop percentages—mirroring Genie 2’s Figure 2.", "limitations": "- Reliance on pLDDT as a noise oracle\nThe method equates AlphaFold2 confidence with corruption level; when pLDDT is poorly calibrated (e.g., false-high scores on mis-threaded regions or low scores on well-modelled flexible loops) the ε-merging schedule injects the wrong amount of noise, limiting fidelity for those motifs.\n- Dataset-inherited AlphaFold bias\nTraining almost entirely on AF2 predictions means the generator learns AlphaFold’s statistical prior rather than experimental structure distributions, potentially reproducing AF2 hallucinations or over-confident helices/loops absent in PDB data.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 4, "strengths_and_weaknesses": "### **Strengths**\n\n- **Methodological novelty** – The paper is the first to *generalise ambient diffusion to arbitrary, unknown corruption processes* by introducing the ϵ-merging-time concept and a per-sample noise schedule.\n- **Low-quality data usage** – By mapping AF2 structure’s pLDDT to an adaptive diffusion start-time, the model **learns from low-confidence predictions instead of discarding them**, turning previously unusable data into a driver of diversity and designability gains.\n- **Geometric re-clustering dataset** – Re-clustering 1.29 M AFDB representatives *for geometric rather than evolutionary similarity* yields a balanced 292 K-structure set that covers folds more uniformly; the procedure (TM-Align 0.5, 0.75 coverage, etc.) is spelt out for replication.\n- **Strong performance** –A 16.7 M-parameter model achieves > 85 % designability *and* diversity up to 700 aa and still 68 % at 800 aa—beating Proteína by 26 / 91 pp at 700 aa and establishing a new Pareto frontier on ≤ 256 aa sequences.\n\n### **Weaknesses**\n\n1. **Loss derivation is mostly intuitive.**\n    \n    Although the paper frames “ϵ-merging time” as a principled way to handle unknown corruption, it never derives the final ambient-diffusion loss from first principles. A concise mathematical induction (or at least a sketch) would clarify why the chosen loss is sound.\n    \n2. **Underspecified mapping from pLDDT to noise.**\n    \n    The critical function *f*(pLDDT) and its three-bin implementation are hand-tuned; no ablation or sensitivity analysis justifies the choices. Without empirical evidence the method may over- or under-weight certain confidence ranges.\n    \n3. **No quantitative evidence for helix bias.**\n    \n    The authors acknowledge the model “still favours alpha-helical structures” but supply no numbers. Reproducing Genie 2’s Figure 2 (helix/strand ratios vs. natural proteins) would make the bias—and any progress—transparent.\n    \n4. **Missing dataset-vs-method ablation.**\n    \n    Two innovations are introduced simultaneously: (i) geometric re-clustering of AFDB for diversity and (ii) ambient training on noisy structures. The paper lacks an ablation table to separate their individual contributions.", "was_revised": true, "final_justification": "Given the strength of the theoretical derivation and the robustness of the noise mapping mechanism, I believe this paper holds significant value and should be accepted.", "rebuttal": "We are pleased that the Reviewer appreciated the novelty of our approach, the motivation, and the strong experimental performance of our method. The Reviewer has concerns regarding: i) the theoretical validity of our loss, ii) limited ablations about a) our mapping function and b) our dataset reclustering, and iii) missing evaluations on secondary structure. We provide clarifications and numerous ablations and evaluations to address these concerns.\n\n* We provide a derivation of our loss function from first principles.\n* We ablate the choice of the mapping function by providing:\n    * Robustness analysis to mispecification\n    * More bins\n    * Continuous generalizations\n* We ablate the dataset reclustering and the Ambient loss separately.\n* We show improvements over the prior state-of-the-art on secondary structure evaluation.\n\n### Loss Derivation\n\n**Reviewer:**: \"Provide a short formal derivation of the ambient loss [...]\"\n\nLet's use $t_n$ to denote the $\\epsilon$-merging time. Let also $p_0$, $q_0$ be the high-quality and low-quality distributios, respectively. Let's also use R.Vs $X_0, Y_0$ to denote samples from $p_0, q_0$. We know that $\\mathrm{KL}(p_{t_n} || q_{t_n}) \\leq \\epsilon$. The goal is to learn the function $\\mathbb E[X_0 | X_t=\\cdot]$.\n\nIf we had samples from $p_{t_n}$, then it is possible to learn the function of interest, $\\mathbb E[X_0 | X_t=\\cdot]$, without ever seeing a sample from $p_0$. This result has been proven in the paper \"Consistent Diffusion Meets Tweedie\" in the context of diffusion models and relates to the Noisier2Noise method from the Signal Processing community. The idea is that we can show the following identity for all times $t \\geq t_n$:\n\n$\\mathbb E[X_0 | X_t=x_t] = (1 - c_t) \\mathbb E[X_{t_n} | X_t=x_t] + c_t x_t$ (for some $c_t$ that is a function of the noise level).\n\n(see Consistent Diffusion Meets Tweedie, p14, Eq. A28.)\n\nThe proof of this identity is quite easy: we can apply Tweedie's formula twice for the R.V. $X_t$, one expressing it as a fuction of $X_0$ and one expressing it as a function of $X_{t_n}$. Using this identity and the definition of the conditional expectation as the best denoiser in l2 sense, we arrive at the objective we have in the paper.\n\nThe only issue in all this discussion is that we don't have samples from $p_{t_n}$, we have samples from $q_{t_n}$. Hence, we can only learn $\\mathbb E[Y_0 | Y_t = x_t]$ through $\\mathbb E[Y_{t_n} | Y_t = x_t]$ for all times $t \\geq t_n$. How far is $\\mathbb E[Y_{t_n} | Y_t = x_t]$ from the desired $\\mathbb E[X_{t_n} | X_t = x_t]$? The answer is not much, because of the $\\epsilon$-merging. We can exactly bound this by using Girsanov's theorem that expresses the KL error as an error of the conditional expectations (For a reference, see the work Sampling is as easy as learning the score, page 11, Equation 5.4 of the arXiv) Hence, since the KL error is bounded, the same holds for the errors of the conditional expectations.\n\nWe hope this proof sketch makes sense. We will add a detailed derivation in the Camera Ready version.\n\n### Secondary Structure Evaluation\n\n**Reviewer**: \"Quantify secondary-structure composition—e.g., helix/strand/loop percentages—mirroring Genie 2’s Figure 2.\"\n\nFollowing the Reviewer’s recommendation, we systematically evaluate the Secondary Structure Proportions of our generated proteins. Specifically, we first use biotite (as in Proteina) to assign secondary structure labels to all the generated proteins. Then, we look at the designable PDB files, we calculate the percentages of alpha/beta/loops, and then we average those over all designable PDBs. The results are shown below:\n\n| Method             | α ↓  | β ↑  |\n|--------------------|------|------|\n| Genie2             | 72.7 | 4.8  |\n| Proteina MFS scale 0.35           | 71.6 | 5.8  |\n| Proteina MFS scale 0.45           | 68.1 | 6.9  |\n| Proteina MFS scale 0.50           | 67.0 | 7.2  |\n| Ambient scale 0.5        | 69.9 | 7.9  |\n| Ambient scale 0.4        | 66.6 | **9.5** |\n\n\nAs shown, Ambient Protein Diffusion generates proteins with more beta sheets and loops compared to Proteina and Genie2, illustrating progress towards designing more natural proteins.\n\n#### SS conditional model \nOver the past two months (since the submission), we further trained a model that can be conditioned on a per-residue SS label. As we increase the Classifier Free Guidance strength towards beta sheets, this model generates proteins with more interesting SS structure:\n\n| Strength Setting | α-Helix (%) ↓ | β-Sheet (%) ↑ |\n|------------------|---------------|----------------|\n| 0.2              | 82.1          | 1.5            |\n| 0.4              | 61.8          | 11.4           |\n| 0.6              | 30.3          | 33.6           |\n| 0.7              | 21.7          | **36.1**       |\n\nWe plan to make these models available together with the code release upon acceptance of our work. We will further add all the Ablations and the Secondary Structure Evaluations in the paper. \n\n\n\n### More Dataset & Ambient Ablations\n\n**Reviewer**:  \"The paper lacks an ablation table to separate their individual contributions.\"\n\nFigure 5 in the paper directly ablates the effect of using Ambient Diffusion, as it shows the effect of having it and not having it on the same exact dataset (reclustered filtered at pLDDT > 70).\n\nWe agree with the Reviewer that we need to separately ablate the need for having a re-clustered dataset. Results below:\n\n| Setting                     | Dataset              | Designability ↑ | Diversity ↑ |\n|----------------------------|----------------------|------------------|--------------|\n| No Ambient                 | Genie2      | **95.2**             | 0.590        |\n| No Ambient                 | Re-clustered         | 81.4             | **0.902**        |\n| Ambient                    | Genie2      | 96.4             | 0.501        |\n| Ambient                    | Re-clustered         | **98.6**         | **0.781**    |\n\nAs shown, **reclustering leads to improved diversity**. Combining the reclustered dataset with Ambient gives the best results.\n\n### Mapping function ablations\n\n**Reviewer**: \"Add ablations for: alternative f(pLDDT) mappings.\"\n\n\n#### Robustness\n\nIn the paper, we used the function `f` defined by the `plddt_to_timestep` mapping:\n\n(90, 0), (80, 300), (70, 900)\n\nProteins with:\n- **pLDDT > 90** are used throughout all steps (0 to 1000).  \n- **pLDDT in (80, 90]** are used from step 300 onward.  \n- **pLDDT in (70, 80]** are used only from step 900 onward.  \n\nWe will now show what happens when we slightly change the function f we used in the paper in two opposite directions.\n\n| `plddt_to_timestep` | Designability | Diversity | Notes |\n|---------------------|---------------|-----------|-------|\n| (80,0) | 95.2 | 0.590 | Genie2 baseline |\n| **(90,0),(80,300),(70,900)** | **98.6** | 0.781 | Paper choice |\n| (85,0),(75,300),(70,900) | 96.4 | 0.780 | Deflated thresholds by 5 |\n| (95,0),(85,300),(75,900) | 96.8 | **0.783** | Inflated thresholds by 5 |\n\n\nAs shown, our method is relatively robust, as small perturbations to the mapping don’t lead to a very substantial change. In fact, the inflated thresholds lead to a model that belongs to the Pareto frontier of Figure 4 in the paper. Running the same model with scale=0.65 leads to another Pareto point, achieving an (86.6, 0.882) designability-diversity pair.\n\n#### Continuous mapping functions and more bins\n\nWe further present continuous generalizations of our original choice. In the paper, we chose a very rough categorization of the proteins into “high-quality”, medium-quality, and “low-quality” for didactic purposes (L191-200). We now try:\n\ni) a piecewise linear continuous generalization.\nii) a sigmoid.\niii) more bins\n\nE.g. before all proteins with pLDDT in (80, 90] were used for times 300-1000. Under i), a protein with pLDDT x in (80, 90] will be used for times t>=300 * (90 - x) / (90 - 80), e.g. a protein with pLDDT 82 is used for times t>=240.\n\n| `plddt_to_timestep`| Designability | Diversity | Pareto         | Notes        |\n|-----------------------------|---------------|-----------|----------------|--------------|\n| (90,0),(80,300),(70,900)    | **98.6**      | 0.781     | ✅ Pareto optimal | Paper choice |\n| Piecewise linear            | 96.2          | 0.827     | ✅ Pareto optimal |              |\n| Sigmoid                     | 98.2          | 0.752     |                |              |\n| (90,0),(85,300),(80,600),(75,900),(70,950) | 95.9 | 0.742 |                | Extra bins 1 |\n| (90,0),(85,200),(80,300),(75,850),(70,900) | 94.2 | **0.858** | ✅ Pareto optimal | Extra bins 2 |\n\nAs shown, by optimizing the mapping function, we can even outperform the results we obtained in the paper. That said, even a simplistic choice, as the ones we opted for in the paper, can yield significant boosts.\n\n### Limitations of pLDDT and AlphaFoldDB\n\n**Reviewer**: \"pLDDT is (sometimes) poorly calibrated\".\n\nThis is true -- pLDDT is known to be unreliable sometimes. We will acknowledge this limitation more strongly in the paper. That said, our method can use any other metric of quality (other than pLDDT). For the purposes of the paper, we chose to use pLDDT because existing pipelines (Genie2/Proteina/RFDiffusion) were filtering proteins based on that score.\n\n**Reviewer**: \"generator might learn AlphaFold’s statistical prior rather than experimental structure distributions\"\n\nIf the quality estimation oracle (in this case, pLDDT) is assumed to be perfect, then that's not going to happen because AlphaFold's bad predictions and hallucinations will be treated as nosiy data. In fact, that's the problem that previous methods are suffering from and our method fixes, at least partially. That said, pLDDT is not perfect (see above) and some biases might remain.\n\n**We believe that our rebuttal strongly addresses the Reviewer’s concerns, and we would be grateful if the Reviewer considers upgrading their score to reflect this.**"}, {"review_id": "9vIjVvtYHn", "reviewer": "Reviewer_Rk4E", "summary": "The paper introduce a framework (”*Ambient Diffusion”*) for training diffusion models that accounts for noisy (low-confidence) structures - which describes a considerable fraction of the predicted structure databases (e.g., from AlphaFold and ESMFold).  Extends recent work on training diffusion models data with a known corruption process by extending it to domains where the corruption process is more complex and a priori unknown.  They consider errors in the predicted structure to be such a process and the pLDDT from AlphaFold to be a reasonable proxy the structural accuracy.\n\nThey build the method on the insight that regardless of how two distributions deviate; adding Gaussian noise causes the KL-divergence between them to contract.  Thus they define a “epsilon-merging time” as the time at which the added noise causes two distributions to have D_KL < epsilon.  They bin structures into low (70≤pLDDT≤80), medium (80≤pLDDT≤90) and high (90≤pLDDT) confidence, and at the start of training apply Gaussian noise at the level is calculated to be the noise at the epsilon-merging time.  Intuitively, this means that the samples have the corruption incorrect predictions “erased” by applying sufficient noise that this error is not longer perceptible.  It follows that one can only train on samples at noise levels above this threshold (so practically, e.g., at low noise you only train on high confidence structures).  It should also be noted that, separate from the *Ambient Diffusion* framework, they also re-cluster the AFDB data aiming for improved “geometric diversity”.\n\nExperimentally, they validate the approach by applying it to a Genie-like model architecture and training, and compare to a suite of structure generation models — most pertinently the current state-of-the-art Proteina.  On unconditional generation (300-800 residues) Ambient Protein outperforms all baseline models by large margin on standard designabilty and diversity metrics, (despite using fewer parameters and less training compute than Proteina).  Unconditional generation of shorter proteins (50-256 residues), they again demonstrate an improved better pareto front on these metrics when varying the temperature of the generative process.  Ablations show that the  *Ambient Diffusion* framework improves over an otherwise identical diffusion-like training.  Finally, they also consider the motif scaffolding benchmark from Genie2, showing reasonable performance - albeit not as clearly state-of-the-art as in the previous experiments.", "questions": "**Q1** How the mapping function, f, (line 203) is calculated in practice? Is it empirically calculated separately for each of the bins (low, medium, high confidence) and so not per-protein but per-bin?  What is the reference distribution against which these are compared when computing the epsilon-merging time?\n\n**Q2** Can you help with my interpretation of the ablations in Figure 5.\n\n**a** As I understand, Ambient vs Baseline is a direct ablation of the proposed framework, showing it has a significant impact on diversity.  Can you present the same results on designabilty also?\n\n**b** Is it possible to infer the impact of the re-clustering of AFDB in isolation from any of the presented results? While Genie2 presumably doesn’t use the re-clustered data, it’s also a smaller model so can’t be taken as a clean ablation.\n\nIn the event that mis-interpretations or oversights in my review are highlighted during the review process, I of course may update my score - though overall I am already a fan of the paper and will be recommending an acceptance.  With suitable clarification on the few points above I would be willing to increase scores for Quality and/or Clarity.", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n\n- The proposed idea is elegant, well-motivated and leads to clear practical performance gains.\n- The experimental evaluation is compelling: suitable metrics and models are chosen and ablations are provided.\n- The paper is very well written, providing good depth of discussion and intuition for several non-obvious technical steps.\n\n**Weaknesses**\n\n- While possibly my misunderstanding, one point where the method description is less clear is relating to the pre-processing of the samples prior to training.  Specifically, it’s not clear to me exactly how the mapping function, f, (line 203) is calculated and what the reference distribution is.  See Q1.\n- The significance of the proposed re-clustering of AFDB could be better discussed.  Specifically, I am not sure this can be inferred from the ablations presented, see Q2.", "was_revised": true, "final_justification": "For the reasons laid out in my review and subsequent disscusion; I keep my original positive recommendation.", "rebuttal": "We are very pleased to see the thoughtful and very positive feedback of the Reviewer! In what follows, we do our best to address the Reviewer's questions and potential concerns. In particular:\n\n* We present further improved motif scaffolding results.\n* We clarify the ablation of Figure 5 and present additional ablations regarding reclustering.\n* We better explain our current choice of the mapping fuction and we provide ablations.\n\n### Mapping function\n\n**Reviewer**: \"it’s not clear to me exactly how the mapping function is calculated. Is it empirically calculated separately for each of the bins and so not per-protein but per-bin? What is the reference distribution?\"\n\nExcellent question and apologies for not having it clear in the first place. The reference distribution is the distribution of \"real proteins\", i.e. proteins observed in nature. In the paper, we approximate this with the set of proteins for which AlphaFold is super confident (average pLDDT > 90). \n\nIdeally, each protein would be mapped to each time separately. The mapping should rely on some proxy for the quality of the protein (e.g. pLDDT). In our paper, we did not use a continuous mapping -- instead we discretized proteins into bins based on their average pLDDT and each bin got an annotation time.\n\nSpecifically, we used the function `f` defined by the `plddt_to_timestep` mapping:\n\n(90, 0), (80, 300), (70, 900)\n\nProteins with:\n- **pLDDT > 90** are used throughout all steps (0 to 1000).  \n- **pLDDT in (80, 90]** are used from step 300 onward.  \n- **pLDDT in (70, 80]** are used only from step 900 onward.  \n\n**We will now provide ablations on this choice of mapping**. We report (designability, diversity) pairs for the short-protein generation benchmark (Figure 4), as it is computationally infeasible to do long protein training for all these studies.\n\nFirst, we show what happens when we slightly change the function f we used in the paper in two opposite directions.\n\n| `plddt_to_timestep` | Designability | Diversity | Notes |\n|---------------------|---------------|-----------|-------|\n| (80,0) | 95.2 | 0.590 | Genie2 baseline |\n| **(90,0),(80,300),(70,900)** | **98.6** | 0.781 | Paper choice |\n| (85,0),(75,300),(70,900) | 96.4 | 0.780 | Deflated thresholds by 5 |\n| (95,0),(85,300),(75,900) | 96.8 | **0.783** | Inflated thresholds by 5 |\n\nAs shown, our method is relatively robust, as small perturbations to the mapping don’t lead to a very substantial change. In fact, the inflated thresholds lead to a model that belongs to the Pareto frontier of Figure 4 in the paper. Running the same model with scale=0.65 leads to another Pareto point, achieving an (86.6, 0.882) designability-diversity pair.\n\n#### Continuous mapping functions and more bins\n\nWe further present continuous generalizations. We now try:\n\ni) a piecewise linear function.\nii) a sigmoid function.\niii) more bins\n\nE.g. before all proteins with pLDDT in (80, 90] were used for times 300-1000. Under i), a protein with pLDDT x in (80, 90] will be used for times t>=300 * (90 - x) / (90 - 80), e.g. a protein with pLDDT 82 is used for times t>=240.\n\n| `plddt_to_timestep`| Designability | Diversity | Pareto         | Notes        |\n|-----------------------------|---------------|-----------|----------------|--------------|\n| (90,0),(80,300),(70,900)    | **98.6**      | 0.781     | ✅ Pareto optimal | Paper choice |\n| Piecewise linear            | 96.2          | 0.827     | ✅ Pareto optimal |              |\n| Sigmoid                     | 98.2          | 0.752     |                |              |\n| (90,0),(85,300),(80,600),(75,900),(70,950) | 95.9 | 0.742 |                | Extra bins 1 |\n| (90,0),(85,200),(80,300),(75,850),(70,900) | 94.2 | **0.858** | ✅ Pareto optimal | Extra bins 2 |\n\nBy optimizing the mapping function, we can even outperform the results we obtained in the paper. \n\n### Clarifications on Figure 5 and Data ablations\n\n**Reviewer**: \"Can you help with my interpretation of the ablations in Figure 5.\"\n\nApogologies for not having it as clear in the paper. Figure 5 compares **three models**:\n\n1. **Original Genie2**  \n   Trained on short proteins with the original Genie2 dataset (pLDDT > 80 filtering, no reclustering).\n\n2. **Improved Genie2 (Baseline w/o Ambient)**  \n   Trained on longer proteins using the **re-clustered data, filtered at pLDDT > 70**.\n\n3. **Ambient Diffusion**  \n   Trained on longer proteins using the **re-clustered data** filtered at pLDDT > 70,  \n   *plus* the Ambient methodology for utilizing low-quality pLDDT samples.\n\nIn summary, this figure **fixes the dataset** (re-clustered, pLDDT > 70) and **ablates the Ambient methodology**.\n\n**Reviewer**: \"Can you present the same results on designabilty also?\"\n\nWe present Designability ad Diversity numbers for Original Genie2, Improved Genie2, Proteina and our Ambient Protein Diffusion below (shown as (designability, diversity)):\n\n| Length | Original Genie2 | Improved Genie2 | Proteina     | Ambient Protein Diffusion |\n|--------|------------------|------------------|--------------|----------------------------|\n| L300   | (81,90)          | (93,93)          | (93,55)      | (90,89)                    |\n| L400   | (60,60)          | (79,79)          | (85,60)      | (92,92)                    |\n| L500   | (20,20)          | (71,71)          | (82,65)      | (91,91)                    |\n| L600   | (2,3)            | (51,51)          | (81,55)      | (87,87)                    |\n| L700   | (1,0)            | (30,30)          | (68,45)      | (86,86)                    |\n| L800   | (0,0)            | (25,25)          | (55,47)      | (68,68)                    |\n\nAs shown, **our Ambient Protein Diffusion model massively outperforms all baselines.**\n\n#### Additional novelty numbers\n\nWe further report novelty numbers for the models of the paper (in short and long generation) to truly show that our model can generate unique proteins:\n\n| Setting                   | Model                    | PDB Novelty ↓ | AFDB Novelty ↓ |\n|---------------------------|--------------------------|----------------|-----------------|\n| Long Protein Generation   | Ambient Protein Diffusion | **0.682**      | **0.740**       |\n|                           | Proteina                  | 0.836          | 0.883           |\n| Short Protein Generation  | Ambient Protein Diffusion | **0.774**      | **0.848**       |\n|                           | Proteina                  | 0.832          | 0.891           |\n\n### Data Ablations\n\n**Reviewer**: \"is it possible to infer the impact of the re-clustering of AFDB in isolation?\"\n\nWe agree with the Reviewer that we need to separately ablate the need for having a re-clustered dataset. Results below:\n\n| Setting                     | Dataset              | Designability ↑ | Diversity ↑ |\n|----------------------------|----------------------|------------------|--------------|\n| No Ambient                 | Genie2      | **95.2**             | 0.590        |\n| No Ambient                 | Re-clustered         | 81.4             | **0.902**        |\n| Ambient                    | Genie2      | 96.4             | 0.501        |\n| Ambient                    | Re-clustered         | **98.6**         | **0.781**    |\n\nAs shown, **reclustering leads to improved diversity**. \n\n### (Bonus): Improved motif scaffolding results\n\nIn their summary, the Reviewer mentions: \"[the authors] consider the motif scaffolding benchmark from Genie2, showing reasonable performance - albeit not as clearly state-of-the-art\"\n\nWe investigated this and we noticed that **the scaffold length is not fixed for our baselines, and this length impacts the number of unique successful structures.**\n\nIn general, for a given motif, the models produce higher numbers of unique successes for longer lengths. In the paper, the numbers reported for Ambient are using the same lengths as Genie 2. We generated samples using 1.5x the average length Genie 2 uses for each motif, and **the number of sucesses icreases from approx. 2K to approx 4K (almost doubles!).**\n\n**Regarding inconsistencies:** For 5TPN, RFDiffusion sets the length to be between 39 and 99 residues, while Genie 2 generates samples between 50 and 75 residues. For 1QJG, Proteína sets the length range to be 95-152, while Genie 2 sets it to 53-103. The lengths used for the other motifs are not provided for either RFDiffusion or Proteína. We cannot fairly compare the performance without sampling the same lengths.\n\nResults for 1.5x legths are shown below:\n\n| Motif      | Genie2 Length | 1.5× Length |\n|------------|------|------|\n| 6E6R_long  | 510  | 720  |\n| 6EXZ_long  | 417  | 848  |\n| 6E6R_med   | 220  | 633  |\n| 1YCR       | 113  | 459  |\n| 5TRV_long  | 73   | 102  |\n| 6EXZ_med   | 51   | 490  |\n| 7MRX_128   | 33   | 23   |\n| 6E6R_short | 16   | 215  |\n| 5TRV_med   | 27   | 109  |\n| 7MRX_85    | 10   | 42   |\n| 3IXT       | 3    | 27   |\n| 5TPN       | 6    | 40   |\n| 7MRX_60    | 1    | 10   |\n| 1QJG       | 2    | 2    |\n| 5TRV_short | 1    | 10   |\n| 5YUI       | 0    | 9    |\n| 4ZYP       | 4    | 13   |\n| 6EXZ_short | 1    | 17   |\n| 1PRW       | 1    | 1    |\n| 5IUS       | 1    | 1    |\n| 1BCF       | 1    | 2    |\n| 5WN9       | 1    | 2    |\n| 2KL8       | 1    | 1    |\n| 4JHW       | 0    | 0    |\n| **Total**  |1923  |3776  |\n\n**We believe that our rebuttal strongly addresses the Reviewer's questios**. If so, we would be very grateful if the Reviewer considers further reinforcing their support for our work. We remain at the Reviewer's availability if there are any remaining concerns."}]

Author rebuttal:

Meta-review: This paper introduces Ambient diffusion for proteins. All reviewers agree that the data engineering and new loss function lead to robust gains across in silico benchmarks. There were several questions regarding ablations of the map $f$ as well as understanding secondary structure diversity. The authors have answered point 1.) with new experiments, and shown that with guidance $\beta$-sheet diversity can be improved. As a result, the use of Ambient diffusion can be leveraged for all future protein diffusion models. However, it is unclear to what extent the in silico gains will be reflective of actual wet lab performance, as AFDB is itself inherently biased. Despite this, in the context of NeurIPS I recommend acceptance with Spotlight.
Decision: Accept (spotlight)