CryoNet.Refine: A One-step Diffusion Model for Rapid Refinement of Structural Models with Cryo-EM Density Map Restraints
Authors: Fuyao Huang
Xiaozhu Yu
Kui Xu
Qiangfeng Cliff Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Protein structure refinement; Cryo-electron microscopy; Deep learning; Density-guided refinement; Geometric restraints; Diffusion model
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)

Abstract: High-resolution structure determination by cryo-electron microscopy (cryo-EM) requires the accurate fitting of an atomic model into an experimental density map. Traditional refinement pipelines like Phenix.real_space_refine and Rosetta are computationally expensive, demand extensive manual tuning, and present a significant bottleneck for researchers. We present CryoNet.Refine, an end-to-end, deep learning framework that automates and accelerates molecular structure refinement. Our approach utilizes a one-step diffusion model that integrates a density-aware loss function with robust stereochemical restraints, enabling it to rapidly optimize a structure against the experimental data. CryoNet.Refine stands as a unified and versatile solution capable of refining not only protein complexes but also nucleic acids (DNA/RNA) and their assemblies. In benchmarks against Phenix.real_space_refine, CryoNet.Refine consistently yields substantial improvements in both model–map correlation and overall model geometric quality. By offering a scalable, automated, and powerful alternative, CryoNet.Refine is poised to become an essential tool for next-generation cryo-EM structure refinement. Web server: https://cryonet.ai/refine; Source code: https://github.com/kuixu/cryonet.refine.

Published as a conference paper at ICLR 2026
CRYONET.REFINE: A ONE-STEP DIFFUSION MODEL FOR RAPID REFINEMENT OF STRUCTURAL MODELS WITH CRYO-EM DENSITY MAP RESTRAINTS
Fuyao Huang² 2.1 Xiaozhu Yu
Kui Xu
Qiangfeng Cliff Zhang!
1 State Key Laboratory of Membrane Biology, Beijing Frontier Research Center of Biological Structures, Tsinghua-Pekee Peking Joint Center for Life Sciences, School of Life Sciences,
Tsinghua University, Beijing, China
2 State Key Laboratory of Membrane Hangzhou, China
Structure and Artificial Intelligence Biology Branch,
3 State Key Laboratory of Membrane Biology, Beijing Tsinghua Institute for Frontier Interdisciplinary Innovation, Beijing, China
f These authors contributed equally to this work. Correspondence: xukui. 201 60t seegtsiinnuuuaaaa org. en, gczhang@ttiinghua edu. en
ABSTRACT
High-resolution structure determination by cryo-electron microscopy (cryo-EM) requires the accurate fitting of an atomic model into experimental density map. Traditional refinement pipelines like rellii..eellssceeeefieie and Rosetta are computationally expensive, demand extensive manual tuning, and present significant bottleneck for researchers. We present SyooNet.Refinee an end-to- end, deep learning framework that automates and accelerates molecular strue- ture refinement. Our approach utilizes a one-step diffusion model that inte- grates density-aware loss function with robust stereochemical restraints, abling it to rapidly optimize a structure against the experimental data. Cry- oNet.Refine stands as unified and versatile solution capable of refining not only protein complexes but also DNA/RNA-protein complexes. In benchmarks against Phenix. space spaccereffine, CryoNet. Refine consistently yields substantial improvements in both model-map correlation and overall model geometric met- rics. By offering scalable, automated, and powerful alternative, CryoNet. Refine is poised to become an essential tool for next-generation cryo-EM structure refinement. Web server: lattps:// http://ntt...reeeieeeeee/ Source code:
attps: https://github. com/ www..//ww..ccccoceeee.....eeeeee refine
INTRODUCTION
Cryo-electron microscopy (cryo-EM) has emerged as a revolutionary technique in structural biol- ogy, enabling the determination of macromolecular structures, including numerous crucial biologi- cal complexes, at unprecedented resolution (Kühlbrandī) 2014; Nogales & Eva 2016). The typical cryo-EM workflow involves several sequential stages: sample preparation, electron micrograph ac- quisition, particle picking, three-dimensione (3D) reconstruction, atomic model building. and final structure refinement. Despite these advancements, persistent challenge in cryo-EM remains the inherent low signal-to-noise ratio (SNR) and the pervasive conformational dynamics of biological samples. These factors often lead to low-resolution cryo-EM density maps from 3D reconstruc- tion, and even high-resolution maps frequently exhibit low-resolution densities at peripheral and/or flexible regions. Such limitations severely compromise the effectiveness of atomic model building tools, including traditional approaches like (Xu et al.) 2019). DeepTracer(Piab et al.) 202T), CryoNer(httts:: /rronet......././//..e ..)), and even more recent breakthroughs like ModelAngelolDaman al. 2024). This result in fragmented
model (Afonine et al. 2018a). A2-Net
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incomplete structures, incorrect identification of amino acid or nucleic acid types, and in extreme cases, the inability to complete atomic model building, often necessitating integration with orthogo nal data sources like RNA-seq for structure discovery BaacoveryWWangg...oo et al. 2024 2025).
Due to the limitations mentioned above, atomic model refinement becomes a crucial step to follow initial atomic model is built. This phase meticulously adjusts the atomic coordinates of each amino acid or nucleic acid within the model, typically employing both automated and manual interactive tools. Automated tools, exemplified by Phenix.real saacl_spae__ree (Afonine et al.) (0188), are highly versatile, capable of refining not only protein structures but also DNA and RNA. It in- corporates comprehensive library of structural restraints, including secondary structure, rotamer, and Ramachandran plot. By iteratively optimizing the stucture through simulated annealing and sampling from vast conformational spaces, seeks a subset of models that best fit the cryo-EM density map, ultimately yielding structure with excellent geometric metrics and high model-map correlation coefficients. Concurrently, interactive tools like CootEmsley Cowtan 2004) provide structural biologists with user-friendly interfaces to visualize poor geometry for convenient manual adjustments. Coot further allows users to dynamically adjust the weights of local density regions with unbalanced quality, offering effective real-time constraints during manual refinement. While highly effective, both automated and manual methods often require "case-by baasebby-case" parameter tuning by experts. The process of cryo-EM refinement is in urgent need of a flexible, robust and fully auto- mated method Leveraging the powerful capabilities of modern Al approaches thus holds immense prospect for developing superior cryo-EM refinement tools.
The landscape of AI in structural biology has been dramatically reshaped by recent advancements in generative models, particularly diffusion models, which excel in protein generation, design, and structure prediction. Breakthroughs like Alphafold3(Abramss)) et al. 2024), RFDiffusion Watson al., 2023), and (Igraaamn et al., 2023) exemplify their exceptional ability to generate diverse and high-quality structures for various biomolecules, including proteins, DNA, and RNA complexes. Beyond single-chain protein prediction, where models like (olluFolll2TTuppee et al,, }. RoseTTAFold (Baek et al.) 2021), and ESMFFol(Lin et al.] 2023) have achieved remark- able accuracy, diffusion-basee methods are extending to protein- protein interactions, protein protein-small molecule complexes, and DNA/RNA complexes (Back et al.) 2021 1 2023 Wohlwend et al. 2025
Passaro et al., 2025). Notably, AlphaFold3 has moved beyond predefined fixed bond lengths and angles from A AlphaFold2, by learning these geometric constraints directly from PDB data using dif- fusion models. This includes accurately capturing geometry features like the planarity of benzene rings in amino acids. However, significant limitation of these generative methods is that while they produce geometrically plausible structures, they often exhibit suboptimal performance on var- ious detailed geometric metrics and, crucially, do not natively support refinement under the direct restraints of experimental data, such as cryo-EM density maps. Applying the robust generative abil- ity of diffusion models to cryo-EM data-restraint refinement thus offers a transformative pathway to substantially improve structure quality and overcome the reliance on laborious, parameter-heavy traditional or manual refinement workflows.
(a)
Difiuten
Cryo-EM density map
Input
Refiied atomic model
Cryo-EM map +input model
Cryo-EM map Refined model
atomic model
Recycling
Figure 1: (a) Workflow of CryoNet. Atomic models are colored by model-map correlation coefficients (CC), with blue indicating high CC and red indicating low CC. (b) The input atomic model. refined atomic model within Eryo-EM density map.
To address these limitations, we introduce CryoNet Refine, novel one-step diffusion model de- signed for cryo-EM atomic model refinement Figure (a). CryoNet. Refine pioneers the integration of advanced atomic generation principles, inspired by the capabilities seen in AlphaFold3, into comprehensive refinement framework. Taking a cryo-EM density map and an atomic structure as in- put, Atom encoder first extracts intricate features from the structure to be refined. Concurrently, Se- quence embedder encodes atomic type information derived from the input molecular sequence. The The Pairformer module follows the (Pasaaoo et al. 2025) perform cross-attention between the
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atom and the sequence embeddings. These representations are then fed into one-step diffu- sion module, which iteratively generates the refined atomic structure. The refinement process is guided by novel designed density loss and set of geometry losses, facilitating iterative optimiza- tion of the atomic model. CryoNet.Refine achieves the first successful atomic structure refinement under the direct constraints of experimental cryo-EM density maps and the guidance of standard geometry metries within a neural network framework (Figure (b)). Experimental benchmarkds demonstrates significant improvements over Phenix. real rewarrraaaaaaae wwwpssppeeeeeeeeeeeee on both protein-protein and DNA/RNA- -potein complexes, showcasing its exceptional performance and broad applicability. Our work presents four main contributions:
(1) We propose the first Al-based method for cryo-EM atomic model refinement, leveraging a deep neural network-based one-step diffusion module.
(2) We develop novel parameter-free and differentiable density generator that can produce simu- lated density maps from the generated atomic model. This innovation enables us to design an effective density loss, marking the first time that density map correlation can be directly utilized as a loss function to guide neural network training.
(3) We introduce set of differentiable geometry loss functions specifically tailored for guiding the generation of geometrically plausible macromolecular structures, which also offer valuable guidance for protein design and protein structure prediction models.
(4) We conduct extensive evaluation of CryoNet. Refine against Phenix. real space _refiee on cryo- EM datasets, showing a marked improvement in structural quality across various metries.
2 RELATED WORK
In this section, we review the state-of-the-art methods in cryo-EM atomic model refinement and structure modeling, highlighting both traditional and emerging Al-driven approaches.
Cryo-EM atomic model refinement. Cryo-clectron microscopy (cryo-EM) has revolutionized structural biology, enabling the determination of macromolecular structures at near-atomic reso- lution. However, the initial cryo-EM density maps often require subsequent atomic model refine- ment to achieve biologically meaningful and geometrically accurate structures. Traditionally, atomic model refinement methods can be broadly categorized into automated and manual approaches. Au- tomated tools, such as and [SOoDE(Crol] 2018), leverage various geometric restraints (e.g.. bond lengths, angles, dihe- dral angles) and force fields to drive atomic models to fit to density while maintaining stereochem- ical integrity. While these methods can be powerful and yield highly refined structures and, with expert '"aaeeby-case" parameter tuning, their extensive parameter sets and specialized workflows often present a steep learning curve for non-expert users. In parallel, manual refinement tools like Coor(Emsley & Cowtan| 2004)offer powerful interactive visualization capabilities, allowing researchers to meticulously adjust individual amino acid residues or local regions directly within the density map. These tools provide unparalleled control and flexibility, enabling highly precise adjustments. Nevertheless, manual refinement notoriously inten-inteesive, coneuconu,,ing and similarly demands significant expert knowledge, making it bottleneck for high- thghtthroughput struc- ture determination.
Afonine et al., 2018b), Rosetta Wang el al. (2016),
Protein Structure Refinement. More recently, the field has seen surge of interest in artificial intelligence (Al)-driven methods for Protein Structure Refinement. Approaches such as DeepAcc- Hirraumaa et al.) [022]) GNNnefineeinng Xu 2021). and AtomRefine Wu et al. (023) employ neural networks, typically 3D convolution neural networks and Graph Neural Networks (GNNs), to learn intricate geometric features of protein backbones and side-chains. These methods aim to predict corrections or refine atomic positions based on learned structural patterns. A key characteris- tie of these existing Al-based refinement techniques is their primary reliance on structural learning, often from large databases of known protein structures. Consequently, the refined structures are fundamentally predictions of geometrically plausible conformations. A critical limitation, however, is the general absence of direct integration with experimental cryo-EM density maps during the dif- ferentiable optimization process. This disconnect means that the final predicted structures, while potentially ideal in terms of stereochemical geometry, frequently do not optimally match experi- mental data. Currently, there is a notable gap in the literature for neural network- based methods that support differentiable refinement under the direct constraint of cryo-EM experimental data.
Diffusion models for structural generation. The advent of diffusion models has marked a signifi- cant paradigm shift in generative AI, demonstrating remarkable capabilities in complex data gener-
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ation, including protein structure prediction and design. Diffusion models, exemplified by architec- (antfnn tures like RFDiffusion Watson et al. 2023) for de novo protein design and AlphaFold((Abrmmae
et al. 2024) for biomolecular interaction structure prediction and, excel at learning atom distribu- tions and generating diverse, high-quality biomolecular structures. Their success in protein structure generation is largely attributed to their ability to capture global and local structural features, implic- itly enforeing geometric characteristies like bond lengths and angles, thus generating models with high stereochemical quality. These models have shown exceptional proficiency in maintaining geo- metric fidelity in generated structures. Leveraging the strong structural priors and generative capa- bilities of diffusion models could offer a novel avenue for cryo-EM structure refinement, particularly if their powerful learning frameworks could be adapted to integrate and be driven by experimental cryo-EM density information in a differentiable manner.
METHODS
3.1
CRYONET. REFINE FRAMEWORK
CryoNet.Refive is an end-to-end deep learning framework designed for the atomic model refinement of macromolecules directly against experimental cryo-EM density maps Figure (a). The refine- ment process begins by taking an experimental cryo-EM density map (dg) and an initial atomic structure (zo) as input. Atom encoder first processes the input structure to extract pairwise features (z) for each atom. Concurrently, Sequence embedder encodes atomic type information (s) derived from the input molecular sequence. These encoded representations (2,8) along with the initial atomic structure (zo) are then fed into one-step Diffusion Module to generate refined atomic structure (.1). Subsequently, the density generator takes the refined structure (x:) as input to produce a simu- lated density map (d₂). A designed density loss (Leen) is then calculated by comparing this simulated map (d1) with the input map (do)- Simultaneously, a Geometry loss (gooo) is computed hased on the refined structure (x,). These two losses are then weighted and summed to form the total loss (C), which is backpropagated to update the parameters of the diffusion module. Crucially, this workflow represents test-time optimization strategy rather than static inference pass. For each specific case, the network undergoes this iterative training-and sratinn-and-ppttnne anddoopiimiztiion loop to fine-tune the parameters of the diffusion module, thereby customizing the atomic structure against the experimental density map and geometric constraints. This process constitutes one refinement cycle. After n such cycles, the final refined atomic model, xy,- obtained. Our network was first initialized with the parameters of Boltz-2 (Passaro et al. 2025). PyTorch implementation of AlphaFold3, followed by training with a composite loss function including two components: one measuring experimental data fidelity and the other introducing geometric restraints. The network trained until convergence, yielding the generated atomic structures that are in high agreement with the experimental data while satisfying geometric constraints.
One-step diffusion module. The atomic structure generator is designed as a one-step diffusion model. Unlike the diffusion module in AlphaFold3 that requires hundreds of sampling steps, one- step diffusion models represent a major development in generative AI, leveraging techniques like Knowledge DistillationMMeng et al. (2022) and Consistency Models(Song al. (023)) (as explored in (Wu et al.] 2025)) to compress the generation process and reduce computational bottlenecks. We have observed that the one-step diffusion module possesses a key advantage: it can easily incor- porate features from experimental data and geometric restriants, into the generation process. This one-step design effectively and efficiently respects the given guidance, generating accurate results that align tightly with the restraints. Figure (b) shows the refining atomic model trajectory colored with model-map correlation coefficients.
Concretely, the refining process is performed by training the network under preconditioned pa- rameterization following (Karras et al. 2022), and finally producing the refined coordinates & as:
X = (o) Xg + (o) Fol (o) Croise (0), C)
(1)
where Cskip= Cout and Cour denote coefficients in the preconditioned forward (opuleeAAppediix C and Fo is a parameterized neural network in it. C denotes conditioned features derived from encoded structural features $ and z. This preconditioned update ensures that the one-step refinement pre- serves the theoretical properties of multi-step diffusion while collapsing the stochastic process into a deterministic, single-step prediction.
Restraints of density map and structure geometry. CryoNet.Refine employs density generator
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Cry
HEDOO CHOOOEE
module
(Cne ens)
Pa slerrar
Denaty
Treat
Counsdyylas
Figure 2: (a) Overview of the CryoNet. framework. The Rryfnet,Refine Network consists of five modules: Atom encoder. Sequence embedder. Pairformer module, Diffusion module, and Density generator. The input atomic model is first processed by the encoders, and the resulting features are fed into a one-step diffusion module to generate an initial refined atomic model. Sub- sequently, the Density generator creates synthetic density map, which is used to compute density loss against the input density map and geometry loss based on geometry restraints. These losses are then backpropagated to optimize the diffusion module, while the atomic model is further refined through multiple recycle steps until convergence. (b) Model-mal mape correlation coefficient trajectory over 234 recycling CryoNet. iterations on the structure of the human concentrative nucleoside transporter (NT3((ank)) The input density map is EMD-0775, the input atomic model is pre- dicted by AlphaFold3.
and two types of loss functions to leverage these restraints. The first type of loss is density loss, derived by compute the correlation between the experimental cryo-EM map and the synthetic map generated from refined atomic model by the density generator (Section 3.2.1I. Another one is set of geometry loss terms imposes stereochemical restraints- such as those derived from Ramachandran plot, rotamer, and bond angle distributions-tt ensure standard structure geometry (Section 3.2.2 Thus the network is trained using recycling strategy that reuses refined outputs as inputs for sub- sequent passes, progressively optimizing the two loss functions for density map agreement and geometry metrics. Together, these novel design choices enable CryoNet.Refine to achieve rapid, generalizable, and experimentally consistent refinement by fully respecting the restraints derived from both the cryo-EM density map and the structure geometry.
3.2
LOss FUNCTIONS
The loss function of CrefNet.Refine consists of density loss and geometry loss, defined as follows:
L = "Iden Lden Lgoor
(2)
Lyeo
"rrma Lrama + Yrot fro + "anglee
Laaggee + TC, Lc, + "viol" L
where y is the weight of each loss. See the detailed definition of these functions in Section 3.2.1 Section 3.2.2] and Appendix To the best of our knowledge, CryoNet.Refine is the first to formulate a differentiable implementation to compute density loss, ramachandran loss, rolamer loss and C3 loss. Although these biological implications have been well-established and recognized indis- pensable for protein structure prediction and atomic model building, prior methodologies have not integrated similar constraints into their nerual network based refinement processes.
3.2. DENSITY LOSS
We compute density loss in two steps: (i) generate a synthetic density map for the refined atomic model; (ii) compute cosine similarity between the input and the synthetic density map to yield the loss term. Both these two steps must be implemented to be fully differentiable. Here we briefly describe how the differentiable density generator works and the formula for density loss function, with more details discussed in Appendix D
Our current density generator is not a neural network but physics- based simulator. Given the grid points m. and all-atom coordinates of the structure model x with N atoms, get the density values
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by constructing Gaussian spheres centering at each atom position:
p(m x
w/e k/m-x,1²
(3)
where w; represents the atomic number of the 7th atom, X is the position vector of the 2th atom, and k is determined by the synthetic density map resolution res as well as the voxel size (both specified as identical to the input experimental map):
k = 8 res/(T v)
(4)
Based on the synthetic density values p(m, x) and those retrieved from the input density map p(m)), can calculate the density loss function Ldon in fully differentiable manner:
p(m,, x) p(m)
Lien
(5)
p x ll
in which the second term is effectively the cosine similarity between p(m, x) and p(m). This Gaussian scattering formula generate the synthetic density map conceptually follows the molmap method in UCSF ChimeraX(Pettersen et al. 2021). but the key difference is that we redesign the entire computation process be fully differentiable using PyTorch. This fully differentiable imple- mentation is essential for our method because it allows the density loss Lien to serve as restraint term for back- pooo-propngttion during each refinement loop. It's also worth pointing out that our density generator achieves better performance than the UCSF ChimeraX (Pettersen et al. (2021) it molmap method, with the averaged correlation coefficients between synthetic and input density maps im- proved from 0.803 to 0.892.
3.2.2 GEOMETRY LOSS
Geometry loss functions are employed to guarantee the stereochemical accuracy and structural va- lidity of predicted proteins by enforcing conformity with established biological restraints. However, previous work has failed to incorporate geometry-related losses such as those for Ramachandran plot, rotamer, and C3 deviation. Therefore, we innovatively implemented these differentiable geom- etry loss functions (ramachandran loss Craaa rotamer loss Lior, C3 deviation loss) in this work.
Ramachandran loss intends exert Ramachandran plot restraints on the predicted protein struc- tures. When computing the Ramachandran loss, all the backbone dihedral angles é and ya will be calculated and evaluated against the Ramachandran criteria retrieved from the Top8000 dataset used by MolProbity (intze et (016))
Crama
Forú (Z) L., T.41, (4-1, Di ai+1),
(6)
where a; denotes the 7th residue's 's amino acid type and F an indicator function (Appendix E.1 that evaluates whether the backbone tripeptide dihedral angles ø, and v; will fall into the outlier region of the Ramachandran plot.
Rotamer loss intends to introduce side-chain rotamer-specife restraints:
Nec
Cyot
F Fx(xx.
where a; denotes the :th residue's s amino acid type and Fx an indicator function (Appendix E. that evaluates whether the side-chain structure of the 4hh residue (determined by the torsion angles Xi E (-T, π is an outlier compared to idealized protein secondary-structe fragments from the Top8000 dataset.
The necessity to introduce C3 deviation loss stems from the importance of C3 atoms, which are side-chain carbon atoms bonded to C. atoms in each amino acid (except glycine). C3 atoms are crucial for describing side-chain orientations, indicating potential incompatibility between protein backbones and side-chains. When the actual position of Cg atom diverges from the ideal position by over 0.25.A, is thus considered as a deviation:
Non.
Lc, =
Σ
1( 1(
Fe,g1 0.25),
(8)

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where Jce E R is the coordinates of predicted C3 atoms while z'ss R is the idealized Cp position computed from positions of other atoms the same amino acid, i.c. Ca. backbone C and backbone N.
EXPERIMENTS
4.1 BENCHMARK
We curated benchmark of 120 complexes (110 protein, 10 SVA/RNAA-Potein with cryo-EM density map resolutions ranging from 1.8 Ato 5.9 A. For each case, initial atomic models were predicted by AlphaFold3 and subsequently refined against the experimental density map by Phenix. real space refine and CryoNet. Refine. Dataset statistics are provided in Figure T0 and Appendix B
4.2 REFINEMENT OF PROTEIN COMPLEXES
We benchmarked CryoNet. Refine against the conventional Phenixxreal_spac saaellsspeeeeeeeleieeeee refinee As summarized Table D Ret.Ne consistently achieves superior scores both model-map correlation coefficients (CC) and model geometric metrics.
Table I: Performance on benchmark of 1 110 protein complexes(t: higher is better, J: lower is better).
Category
Metries
AlphaFold3
Phenix.real space space.refine
CryoNet.Refine
CCmaak
0.38
0.54
0.59
CC COme
0.41
0.53
0.57
Model-map Correlation
0.40
0.55
0.60
CCac 1
0,39
0.55
0,58
Coefficients
CC CCpanka
0.27
0.40
0,45
CCvolume
0.42
0.55
0.60
Angle RMSD (degree))
1.58
0.72
0,36
Cg deviations. Ramachandran favored (%)f
0.03
0.00
0.00
Model Geometric
95.73
96.39
98.92
Ramachandran outlier (%)
0.82
0.02
0.06
Metrics
Rotamer favored (%))
97.08
85,42
98.64
Rotamer outlier (%)
1.08
1.15
0.49
Figure and Figure the performance of CryoNet. across six model-map correlation co- efficients (CC) and model geometric metrics, respectively. Notably, the consistent gains in C'Cmask (0.59 vs. 0.54) and CCme (0.60 vs. 0.55) suggest the refined atomic model achieves more accu- rate main-chain placement within the density map. Regarding geometry, our method consistently achieves superior stereochemistry, virtually eliminating C3 deviations, raising Ramachandran fa- vored percentage to nearly 99% (98.92%), and reducing rotamer outliers by approximately 57% compared to Phenix.real space spuicereffiee (1.15% to 0.49%). Furthermore, Angle RMSD is drastically reduced from the initial 1.58 to 0.37%. These results emphatically highlight that CryoNet Refine simultaneously improves the stereochemical geometry and the agreement to the cryo-EM density map.
Phenie
Refine
CCeaar
CCea
CC.:
OCuure
1.0
0.38
0.41
3.0
0.51
Coac
a
0.
0.6
0.6
0.6
02
02
0.
0.2
Figure 3: Model-map correlation coefficients on protein complex benchmark.
Figure 5 shows that CryoNet. Refine outperforms both AlphaFold3 and Phenix.real space refine in model-map correlation coefficients and model geometric metries.
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Figure 4: Model geometric metrics. (Color gradient: blue for better, red for worse.)
AbphoFardd
Phonicrcol space refic 0.38;
Rryotet 0.87
CCrum CCye 0.00
0.10s
CC -0 (CCo 0.85
DCpe 0.75; CC 0
Resckt 2.40
Angle PMSO 1.54, Cy doy 0.00 te... Ma.7 Pi; famr sut 6.0%%
Angle RMBD 0.66, Cy dow 0.00
Angle RMSO 0.8%; C2 don- 0.00
net. 1215 Hare sut. aa0e:
Famm fac.. soconic itam out.. 0.00%
CARAD
Phantccrest apace Juline
GRAA DND
CGaut = 0.50 Co 0.84;
CC 0.00 Eo 5.12:
CC cani = als
Co 0.53; DCyc 0.52
D. - C. ce 0.88;
C. 37000CCe
#0 chaRro
Angle FMEED 1-ft: Dg der- 0.00:
Angle Hilr - G2 des- dittt
Angle 0,00; C3 des... 0.50X Farra INc... 79P9 iaama cut... OUCO9S:
Hamm 8056 Fhar mut... 0.11%
Farrr thc... 10%: iaams cut... o.cors:
Figure The input atomic models from AlphaFold3, the refined atomic model from Phenix. real space space-refine and CryoNet.Refine the Medicago truncatula HISN5 protein (PDB-7oj5; EMD- 22692) and the human concentrative nucleoside transporter CNT3 (PDB PPDB-6ksw, EMD-0775) com- plex. Inserts in the right panel show that the main-chains and side-chains generated from CryoNet. Refine model align well with the density map.
4.3 REFINEMENT ON ANA/RNA-PROTEE COMPLEXES
We next evaluated CryoNet. DNA/RNA-proted complex. As our current implementa- tion doesn't 't incorporate nucleic acid-specific stereochemical restraints, the assessment exclusively focused on model-map correlation coefficients (CC) as shown in Table 2 Across all metrics, Cry- Refie consistently outperforms both AlphaFold3 and Phenix. spaciiieeelsspeeeeeeee refine, demonstrating substantially improved agreement with experimental densities.
Table 2: Performance on DNA/RNA- complexes.
Category
Metrics
AlphaFold3
reeenix.eul.ppucc.efffn
CryoNet.Refine
CCmask CCbox f
0.40
0.57
0.65
0.49
0.61
0.67
Model- map Correlation Coefficients
CCme
0.45
0,62
0.61
CC2o
0.42
0.58
0.67
CC CCpoaka 1
0.35
0.51
0.60
CCvolume
0.48
0.61
0.69
For DNA/RNA-protein complex, we show model-map correlation coefficients in Figure 6 It can be observed that CryoNet. Refine achieved substantial improvements in both CCmask and CCsc strongly indicating superior performance refinement in both main-chain and side-chain. A repre- sentative study is shown in Figure 7 where AlphaFold3 and Phenix.real www.ceeeesspeeeefieeeeeeeeeeeeee achieve moderate density fitting (CCmasse 0.18 and 0.36, respectively), whereas SeyoNet.Refine attains a markedly higher CCmask 0.72, along with consistent gains across all other CC metrics.
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AlraFaas
Pheric res Spare refie
Cryster Refine
OCoune
0.
0.8
0.6
0.4
0.6
0.1
00
0.
Figure Model map
map correlation coefficients on DNA/RNA-protein complex.
Aphaaoodd CCuast = 0.48 Cu =0 0.65. CC.. 0.40; CC., = 0.48.
Phonicraal space rafine CU = 0.60: CC 0.72 CC... 0.88; u. - 0.66;
CryoNeL.Raloe C'uasat 0.71: CC 0.70% CC 0.70 CC 0.71.
PDR-AWIL EMD-21541
CPNRNIN 01230 0T1216
AlphuFald Cl Cas = 0,50; CC 021 C21;CC,, 0.15,
Phonic.mast space refine CC Qugaus =0 0.35 CCass 0,68;
Prafiee C'raus 0.72: CC 0.70)
CC... 0.4:CC-- 0.35.
CC CC, 0.72.
90
Figure 7: The input atomic models from AlphaFold3, the refined atomic models from Phenix. real_space_reffe refine and CryoNet.Refine are shown on the (as12i(E894A) -rND----DA-AAA (PDB- 6w5c, EMD-21541) and the active-state Dotl bound to the H4K16ac nucleosome (PDB-7k6g, EMD- 22692) complex. Inserts in the right panel show that the main-chains and side-chains generated by CryoNet. Refine align well with the density map.
5 ABLATION STUDY
Results of the ablation study can be found in Appendix F:3 The full CryoNet. configuration achieves the best balance between model-map correlation coefficients and model geometric metrics. Removing individual loss terms leads to distinct degradations in correlation metrics or geometric metrics, confirming the complementary roles of density and geometry loss.
5.1 RUNTIME PERFORMANCE
Runtimetsh
4000
Protei
We benchmarked the runtime of CryoNet. against Phenix.real space refine. SoyNNet.Refine consistently achieves highly efficient performance, whereas Phenix.real real-space space_refine CPU-only support incurs higher computational costs, particularly for large complexes.
2300
2010
Across 120 complexes, CryoNet.Refine ran faster than Phenix.real space_reefine in 65 cases (54.2%). These results underscore that method combines superior accuracy with high efficiency, making it ideal for large-seale, high-throughput cryo-EM refinement.
5000
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6 CONCLUSION
In this work, we present CryoNet.Refine, pioneering one-step diffusion module for cryo-EM atomic model refinement. It critically features novel differentiable density loss and comprehensive geometry metric loss, achieving unparalleled refinement accuracy.
Our framework opens new avenues for the field: the density loss can be broadly applied AI- based atomic model building, while the geometry loss offers essential guidance for protein structure prediction. Specifically. these differentiable constraints are model-agnostic and can complement the implicit priors of foundation models like AlphaFold3. By integrating them into conditional diffusion sampling strategies, future research could bridge the gap between generative priors and the atomic- level stereochemical precision required for high-resolution structures.
CryoNet.Refine thus marks a significant advance for the cryo-EM community, Looking ahead, we aim to extend the specialized geometry loss for DNA/RNA structures and incorporate steric clash loss. We also acknowledge the computational cost associated with per-structure optimization; there- fore, future work will focus on enhancing efficiency through parallel refinement frameworks and faster convergence strategics. Ultmaaely, we intend to demonstrate superior performance on chal- lenging low-resolution density maps, establishing CryoNet. Refine essential tool for structural biology.
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A
NOTATION
Framework
do
Input cryo-EM density map
20
All-atom coordinates of input structure
Sequence Embedding
2
Pairwise Representation
<i = 1, 1.. ,n)
Refined atomic model after the recycle
di 1, m2)
Synthetic density map of refined atomic model 2;
7
Weight for loss function term Lz
Diffusion Module
So, Eman
Noise scaling hyperparameter
Noise scale parameter in diffusion refinement
daata
Data-dependent scale constant (fixed 16), estimated from training distribution
(o)
Skip coefficient in preconditioning
(a)
Output scaling coefficient in preconditioning
(or)
Input scaling coefficient in preconditioning
Cnoise (a)
Noise embedding term in preconditioning.
Auxiliary conditioning features derived from s, 2, and en- coded structural features
Density Loss
Atomic weight
res
Resolution of the input density map
Voxel size of the input density map
rg
Gaussian radius
sg
Radius of the virtual Gaussian sphere
Number of grid points for each atom per axis
x [x x1, x²]
All-atom coordinates of refined atomic models Synthetic density map
d m pl
m = |>, 14, m)
Grid points of density maps
Synthetic density values
p
Density values retrieved from the input density map
Geometry Loss
Amino acid type
Ness Natom: Noodd
Number of residues, atoms and bonds in a structure
0
Bond angles
X
Torsion angles
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B DATASET
Figure I0 summarizes the dataset statistics. The two panels respectively show the number of chains and the number of residues with respect to map resolution. Protein-only complexes display broader diversity in both chain counts and residue numbers, whereas DNA/RNA-protee assemblies tend to be smaller but fall within comparable resolution ranges.
For all targets, input sequences were retrieved from the RCSB Protein Data Bank (PDB). Since Al- phaFold3 imposes practical sequence length limit of =5000 amino acids, we adopted a chain-wise strategy: sequences were segmented at the chain level and truncated if necessary, ensuring that the combined length per case did not exceed 5000 residues. This preprocessing step guarantees com- patibility with AlphaFold3 while preserving the completeness of structural contexts across chains.
For residues with backbone correlation coefficients below 0.1, we applied the ADP-EM local refine- ment tool Garzon el al. 2007) to pre-process the models and improve rigid-body docking.
dResidues Resolution
#Chains Resolution
20
3000
2000
Figure 9: Dataset statistics of density map resolution, number of chains, and number of residues.
C ONE-STEP DIFFUSION MODULE
Classical diffusion models define forward noising process and a multi-step reverse denoising chain (Ho et al. 2020 Song et al. 2020). While powerful, such iterative schemes incur substantial compu- tational cost. Inspired by accelerated sampling approaches such as consistency models (Song al. 2023) and diffusion distillation (Meng et al., 2022). we reformulated diffusion into a deterministic one-step refinement tailored for cryo-EM structural optimization.
Unlike conventional diffusion that begins from Gaussian noise, we initialize directly from the the starting structure Xg-
Refinement is then performed through a preconditioned forward module(Karras et al. 2022):
x; = Cakip( Xo + Cou((a) FolCan (o)xx;; Cnoise (o); C),
with auxiliary conditioning C. Fo is neural network responsible for the scoring mechanism. The other coefficients include:
(a) 0² + data
data
Gout (o)
Odata
(10)
V02 + -
1
(a)
Cnoise (a) log
a
(11)
Va² + o2
The refined structure after the ith recycle is obtained in a single deterministic step:
X; o C,C)
(12)
where the deterministic refinement operator D is instantiated using the preconditioned forward update (Eq. 9Fq.9):
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(8 0,C) = Cskiplo) Xy + (o) (o((anlo)xoo Cnoise (o), C).
(13)
Algorithm One-step Deterministic Refinement in CryoNet. Refine
Require: Initial structure Xo, conditioning C
Require: Hyperparameters: Çu: Smin- d, learning rate
Require: Number of recycling steps n
Ensure: Refined structure Xfinal
1: Initialize model parameters 0
2: for recycle ..2.....1 do
:
3: Step 1: Compute noise level adjustment
4: & <- -(a >0> Emin) & :o:0
5: f E)
6: Step 2: Perform structure update (One-step)
7: Xpred 6- (xo C)
8: Step 3: Compute loss and backpropagate
9: L. t Lidenitt( (Xpred, C) + Lycommetyy (Xpred)
0 -0-11VLL
11: if converged then break
end for
13: return Xgred
Compared with AlphaFold3, which employs multi-step stochastic denoising from Gaussian initial- ization (Abramson et al.) (024)), our formulation collapses the diffusion chain into single deter- ministic refinement. This yields (i) efficiency by eliminating iterative sampling, (ii) stability via input-output preconditioning, and (iii) broad applicability to proteins, DNA/RNAs and complexes.
is important to distinguish between the diffusion sampling mechanism and the workflow. The term "One-step" refers to the efficiency of diffusion sampler (Eq. [3 Unlike stochastic samplers that require hundreds of iterative denoising steps to generate a structure, our preconditioned module maps the initial structure Xu directly to the predicted refined state in single forward pass.
In contrast, "Recycling" refers to the outer test-time optimization loop. Although the sampler is capable of generating structure in step. achieving figh-precision fit to experimental density requires iterative tuning. In each recycle, we perform a one-step forward pass using the fixed input Xo. compute density and geometry losses the output, and backpropagate gradients update the model parameters 0. This iterative optimization allows the diffusion module to progressively customize its weights the specific instance, minimizing the loss over multiple cycles.
C.1 ARCHITECTURAL DIFFERENCES FROM ALPHAFOLD3
While CryoNet.Reiwe initializes its parameters from the weights of Boltz-2, its architectural design and inference workflow diverge fundamentally from the standard AlphaFold3 framework address the specific challenges of cryo-EM refinement. The key distinctions summarized below:
1. Input Initialization: Standard AlphaFold3 is generative model designed for de novo pre- diction, initializing the diffusion process from Gaussian noise (X1- (0, I)) to generate diverse conformations. In contrast, CryoNet. is refinement framework. We initial- ize directly from the initial atomic model, treating as a noisy state that requires correction against the density map.
2. Sampling Trajectory: AlphaFold3 employs a stochastic multi-step sampler to traverse the reverse diffusion process, which is computationally expensive and introduces randomness. CryoNet. Refine reformulates this into a one-step prediction, mapping the input state directly the denoised structure single pass for efficiency.
3. Optimization Paradigm: AlphaFold3 typically operates in fixed-weigh inference mode. Conversely, CryoNet. adopts a test-time optimization strategy. During the refinement loop (Algorithm D}. we explicitly compute gradients from the density and geometry losses
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update the diffusion module parameters (9). This allows the network to learn the specific features of the experimental density map for each individual case.
4. Module Adaptations and Trainability: To specialize for density-guided refinement, we streamlined the modular architecture.
-ulti-sequence alignment (MSA) processing, confidence heads (pLDDT/PAE), and internal architecture-level recycling removed, the method relies on physical density constraints rather than evolutionary information.
The Sequence Embedder, Atom Encoder, and Pairformer are kept frozen to pre- serve robust structural priors derived from pre-training. Only the Diffusion Module is trainable, focusing the optimization capacity solely coordinate adjustment driven by the experimental map.
D DENSITY GENERATOR
Our current density generator builds the target density volume by summing Gaussian functions cen- tered atomic positions with the simulation process specifically tailored to the target resolution. This procedure conceptually follows the molmap implementation in UCSF OhimeraX(Pettersee al. 2021).
density map can be discretized as a group of 4-dimensional vectors [X, p4, V, pl. where m [λ uJ act as grid points that specify certain location and p is the density values at each grid point, with the origin of coordinates nearest to min and farthest to max. For compu- tation of the overlapped region, first locate this region Vm, E S, between the input density map dn and the synthetic density map d; through the coordinate system:
Omii max mm m min))
M Oreo
min O Mi
After locating So, select all the density values within it from do and d, and get their subsets do and d- Thus, the this overlapped region S., our synthetic density values and the input density values will be defined as:
p P= p == Pino
For the implementation of synthetic density map generation, we follow the molmap algorithm in ChimeraX(Petttersnn et al. 2021), utilizing the all-atom coordinates of the refined atomic model at the 8th recycle Z = x x.. x3] and output a box-shaped density map d; = (m, Pi). where ã; E R3 and m, E R3x Nam noting that the parameter stands for the number of grid points for each atom per axis, and its value is obtained by:
rg res/ee(e - v), sg 4.rg, L 2-2-s0
where res is the input density map resolution and v represents voxel size. The key idea here to construct a Gaussian sphere for each atom, with rg and sg respectively meaning Gaussian radius and the radius of a Gaussian sphere. We expect that m, turns out to be a box as small as possible with all-atom coordinates H; inside it well margin of Gaussian sphere around it, so:
m [[min(x))], [min(x))) ),, |in (min(x)?) (x²) ]],
m [[max (29)1, mmxx(=))1 [max((;]]] [ irea M) )/2 + 2 sg + 17, mime = (m.... + m ) v)
miz
m [ sisx) mi.. [ + mic
For each atom per axis(for example the x-axis), we can get density values around the original atom coordinate by applying Gaussian distribution:
(x?)" + ), [
for n E (1, ..., Natom)
p = Wn. exp(
[-sg. 0,-..,,,.)) -sg],
(14)
2
where Wn signifies the atomic weight of the corresponding atom. To combine density values on all directions, each atom will end up with 1 density values:
p
p3 PH
p
(15)
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d
Density generator
Refined atomic model
Synthetic density map
Cryo-EM density map
Figure 10: Data Patterns and Visualizations of the Density Generator Output
The key difference between molmap and our density generator is that we redesign the entire compu- tation to be fully differentiable using PyTorch, which essential for our method because it allows the density loss (controlled by single hyperparameter, "den) to serve as restraint term for back- propagation during the refinement loop.
To evaluate how well the simulated maps agree with input experimental maps, we calculate their cor- relation coefficients across all cases. The average correlation 0.892, significantly improving from 0.803 when using the USCF ChimeraX molmap method. Nevertheless, simulated maps inevitably fall short of capturing the complex characteristics introduced by diverse experimental instruments and imaging conditions. In particular, secondary structure elements, map artifacts, and noise pat- terns in our simulated densities differ from those observed in experimental maps. To address these limitations, future work will explore replacing the simulation-bail based density generator with deep learning basen generative model, which could better reproduce the statistical and structural proper- ties of experimental cryo-EM maps and yield more informative and accurate density loss.
E Loss FUNCTIONS
After collective parameter tuning, the weight values for each component of our loss function are listed in Table
Table 3: Loss function weights
Loss Functions
Weight
Value
Density loss (Lden)
Yden
20.0
Ramachandran loss (Crama)
Trama
500
Rotation loss (Lme)
Trot
500
Angle loss (Cangle)
Yangle
2
Cg loss (Cc,) Violation loss (Eviol)
PCp
50
Vvial
1000
E. RAMACHANDRAN AND ROTAMER LOSS
The Ramachandran plot (Goodman et al. 1970) is 2D graph with angles and &b angles as and y-axis. By plotting the combination of these torsion angles of all residues, it provides insights into whether the conformation sterically favored, allowed outliered.
In order to obtain more updated and more representative protein structures for reference, MolPro- bity(Hintze al., 2016). the widely used validation program for protein structures, curated the Top8000 dataset by filtering and deduplicating high-quality protein structures from the PDB Bank. The release the Top8000 dataset came with their 3-dimensional Ramachandran grids plotting ideal distribution for different kinds of amino acids The z-axis values act density scores mea- suring the frequency for a certain combination of Ramachandran angles.
get the density score for any combination of arbitrary Ramachandran scores and classify them as falling within favored, allowed, or outlier regions, shown in Algorithm 2
Through interpolation of the nearest grid values,
In fact, there are distinct types of Ramachandran plots for different amino acids. including Gly, Val/Ile pre-Pro, trans-Pro Pro, cis-Pro and Ala. How to differentiate them and the rationale behind this categorization are heyond the scope of this paper.
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As for Fx of rotamer loss, the procedure is highly similar to Algorithm except that it requires X angles instead of Φ, Y angles, and performs 4-dimensional interpolation (since each density value corresponds to the combination of four angles)from the rotamer distribution library of Top8000 dataset.
Algorithm 2 Classification of Ramachandran Angle Outliers
Te: The i-th residue coordinates
ag: The amino acid type of the i-th residue
Nes: total number of residues
Srama type = {Gly, Val/Hle, pre-Pro, trans-Pro, cis-Pro, Ala)
r Srama type: categorization Ramachandran angles between 14 144
Ty. density value threshold for Ramachandran category r
count of Ramachandran outliers
Input E 1 IN [01, 02. .NN.
Function getDensity(O), r;);):
R + Ramachandran distribution grids for T;
density Sensity_scoree_e score +- 2DInterpolate [b]] R([Ø), (v))
return density _score
for i = Nres
61, 1b calculateDihedraals (2,-1, ((11)
a,, a;+1)
density score, getDensity @i v..T;)
if density score; < Tr then +++1
end if
return N/N
30c
52
-55
-150
-20
-00
50
300
250
(a) 2D Ramachandran plot (b) 3D Ramachandran distribution
Figure 11: Visualization of Ramachandran distributions
E.2 BOND ANGLE LOSS
Bond angle loss applies geometry restraints chemical bonds and forces them to approach the target values specified by the ideal geometry library. In our implementation, Langle essentially equivalent to the structure's bond angle RMSD value:
Noai
Lanige
A0?
(16)
Nhond
where Nbond counts the number of all chemical bonds inside the whole protein structure, and A0; (-T,, π calculates the minimal angular difference between the predicted angle value 0, and the ideal angle value 0:
A0; arctan(sin(() 0,)/ cos(O, 0,))
(17)
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To identify chemical bonds given all-atom coordinates, follow the algorithm as well ideal bond angle values given by phenix.pdb.interee Antpaaadddbeeeereettttotttttoo et al. 2012 and rewrite the imple- mentation using PyTorch.
E.3
VIOLATION LOSS
Violation loss penalizes steric clashes between nonbonded atoms to prevent potential clashes. We borrow the OpenFold implementation (Ahdritz al. 2024) and follow the definition of (Jumper
et al. 2021
Natan
Liviol
max
8) predd 0),
(18)
where si Speed is the distance of two non-bonded atoms in the predicted structure and sia is the "clash- ing distance" of these two atoms according to their literature Van der Waals radii. Nubpuir is the number of all nonbonded atom pairs in this structure. The tolerance 7 is set to 1.5 A.
F RESULTS
F.1 RECYCLE STRATEGY
65-
Racjei
Figure 12: Model-map Correlation Coefficients (CC) analysis of protein complexes across different recycling numbers (We provide trajectory video over the entire 234 refinement recyclings in sup- plementary material).
The recycling strategy of CryoNet. Refine sets a maximum of 300 iterations combined with an early- stop mechanism. To demonstrate the rationale behind this, we picked a protein structure from our dataset (PDB-óksw) and trace its model-map correlation coefficients (CC) values after each recycle iteration, as shown Figure 12]
This trajectory serves as sensitivity analysis regarding the number of recycling steps, revealing two distinct phases the refinement process:
1. Highh-eenstivityy Phase (Recycles 0- 100): The CC metrics increase sharply, indicating that the model is highly responsive the initial density-aware gradient updates as it resolves major structural conflicts.
2. Robust Convergence Phase (Recycles > 100): The curves plateau asymptotically, showing that the refinement becomes robust and insensitive to additional iterations once the structure matches the density map constraints.
These 4 CC values basically follow similar pattern. Consequently, the setting of 300 iterations provides sufficient safety margin for convergence. while the early-stop mechanism effectively identifies the transition to the plateau phase, avoiding unnecessary computation.
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F.2 DIFFUSION SAMPLING STEPS AND COMPARISON WITH CLASSICAL DIFFUSION
CCan
CCs
0.20
0.19
75
100
125
252
175
200
Figure 13: Model-map Correlation Coefficients (CC) analysis of DNA/RNA- protein complex across different diffusion sampling steps.
To show that one-step diffusion module is improvement over previous diffusion models with multiple sampling steps, we picked a protein structure (PDB-6ksw) and run with 200 steps. The model-map correlation coefficients (CC) values after each step are shown in Figure 13 Each curve has its optimal value at the beginning step and steadily falls when sampling more steps, which demonstrates the efficacy of our one-step diffusion module.
To validate our design choice of one-step diffusion module, we conducted a comparative ablation study against a classical multi-step diffusion approach.
Experimental Setup. For the classical diffusion baseline, we employed a standard stochastic sam- pling trajectory with T 200 steps within one recycle, setting typical for generative protein struc- ture models like Boltz-2 or A/phaFold3. The inference process started from the initial AlphaFold3 prediction. At each step the network predicted the denoised structure, and Gaussian noise was injected according to a standard variance schedule before proceeding to step / 1.
Quantitative Results. illustrated in Figure 13 (which shows the rapid decay of CC values over steps) and quantified in Table the multi-step approach leads to catastrophic degradation in both model-map correlation and geometric integrity. The 200-step sampler yields a CCmask of only 0.30 and introduces severe geometric violations (e.g.. Angle RMSD of 1.66%).
Table 4: Quantitative comparison between CryoNet.Refine (One-step) and Classical Diffusion (200 steps) across 27 cases. The multi-step approach fails to preserve structural biology constraints when applied to refinement tasks.
CryoNet. (One-step)
Classical Diffusion (200 steps)
Category
Metrics
CCmau
0.65
0.30
CChox
0.58
0.35
Model-map
CCme
0.66
0.31
Correlation
CC t
0.63
0.31
Coefficients
CC CCpeaka
0.47
0.24
CCvelume
0.65
0.34
Angle RMSD (*)
0.54
1.66
Cp deviations
0.00
0.00
Model Geometric
Ramachandran favored (%))
98.50
98.63
Ramachandran outlier (%)..
0.10
0.81
Metrics
Rotamer favored (%))
98.58
98.63
Rotamer outlier (%)
0.51
0.18
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Published as a conference paper at ICLR 2026
We suspect that the degradation arises from 2 main factors: (1) We employ deterministic sampler, which intrinsically requires fewer steps; and (2) The diffusion module receives as input an already complete and physically reasonable macromolecular structure, rather than random noise in the training regimes of AlphaFold3 or Boltz-2 for de novo structure prediction.
These findings confirm that for the specific task of structural refinement against density maps, targeted one-step diffusion scheme is far superior to classical multi-step generation.
F.3 ABLATION STUDY
We performed ablation study 27 protein complexes (Table The full CryoNet.Refine figuration achieves the best overall performance between model-map correlation coefficients and model geometric metrics, underscoring the necessity of integrating density- and geometry-awan objectives.
Table Ablation study: how loss functions influence model-map correlation coefficients and model geometric metrics
Category
Metries
Vdeen
0
Yroot
0
CryoNet.Refine
CCmask
0.41
0.65
0.64
0.65
CCbox
0.42
0.58
0.57
0.58
Model-map
CCme
0.42
0.66
0.65
0.66
Correlation
CC2c
0.41
0.64
0.64
0.63
Coefficients
CCpeaks 1
0.24
0.48
0.47
0.47
CCvolume
0.43
0.65
0.64
0.65
Angle RMSD (
0.45
0.41
0.44
0.54
C-beta deviations
0.00
0.00
0.00
0.00
Model Geometric
Ramachandran favored (%)T
99.09
90.75
99.22
98.80
Ramachandran outlier (%)
0.06
2.27
0.03
0.10
Metrics
Rotamer favored (%)f
98.67
98.64
94.48
98.58
Rotamer outlier (%)
0.54
2.11
1.38
0.51
Removing the density loss (rddn 0) leads to pronounced drop across all CC metrics, with CCmask and CCme reduced by over 35%, confirming that the density term is indispensable for guiding accurate model-map fitting. In contrast, omitting the Ramachandran prior (Trama. = 0) preserves correlation coefficients but severely compromises geometry, reducing favored residues from 88.80% 90.75% and inflating outliers more than 20-fold. This highlights the critical role of stereochemical priors in constraining backbone conformations.
The effect removing the rotamer prior (Trot = 0) more nuanced: CC values remain competitive, and Ramachandran statistics are slightly improved, but side-chain packing deteriorates, with favored rotamers dropping 94.48% This indicates that local side-chain restraints complement backbone priors in ensuring chemically realistic conformations.
Together, these results establish three key principles: (i) density loss is essential for achieving high model-map correlation, (ii) stereochemical priors, particularly Ramachandran constraints, safeguard backbone geometry, and (iii) rotamer priors contribute to realistic side-chain packing. The synergy of these components underpins CryoNet.Refine' ability to deliver models that are both density- consistent and stereochemically robust.
F.4 COMPARISON WITH DIRECT NUMERICAL OPTIMIZATION
To investigate whether the generative capabilities of our diffusion model strictly necessary, or the structural improvements are merely due to the proposed differentiable loss functions, we im- plemented pure numerical coordinate optimization baseline. This baseline involves neural networks, no diffusion process, and no learned structural priors.
Experimental Setup. In this baseline, treated the atomic coordinates of the initial AlphaFold3 prediction as learnable parameters (x E R3x Naom), The optimization process was designed to be as close possible to the C inference loop:
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Published as a conference paper at ICLR 2026
Inputs: The initial AlphaFold3 structure and the experimental cryo-EM density map.
Objective Function: We utilized the identical composite loss function used in Cryo- Net.Refine: C = Lden Lgoo employing the exact same weights (7) for all density and geometric terms.
Optimization: The coordinates were updated directly via backpropagation using Stochastic Gradient Descent (SGD) optimizer with momentum of 0.9.
Schedule: To ensure a fair comparison with our diffusion model, we set the maximum number of iterations (recycles) to 300, matching the diffusion inference budget. An early stopping mechanism with a patience of 20 iterations was implemented, along with ReduceLRonP lateau scheduler dynamically adjust the learning rate.
Results. We evaluated this baseline on representative subset 27 protein complexes (Table 6 The results reveal a critical limitation of pure numerical optimization. While the baseline achieves excellent geometric scores (c.g.. the lowest Angle RMSD of 0.27%), fails to effectively the density map, yielding CCmas of only 0.46, which is marginally better than the initial input (0.44) but significantly worse than CryoNet.Refine (0.65).
This indicates that without the generative and exploratory capabilities of the diffusion model, the gradient descent process gets trapped in local minima close to the initial structure. It satisfies the geometric constraints (which are local) but cannot traverse the energy landscape find the global conformation that matches the experimental density. Thus, the one-step diffusion module is essen- tial for balancing data fidelity with biological plausibility.
Table Comparison between CryoNet. and Direct Numerical Optimization (SGD) on a sub- set of 27 protein complexes. The numerical baseline optimizes geometry well but fails to fit the density map.
Phenix. reul-space .refine
Numerical Optimization
CryoNet. Refine
Category
Metries
AlphaFold3
CCmask
0.44
0.61
0.46
0.65
CCbox
0.44
0.55
0.47
0.58
Model-map
CCme
0.45
0.62
0.46
0.66
Correlation
CC.c
0.44
0.61
0.45
0.64
Coefficients
CCpeaka f
0,31
0.44
0.32
0.47
CCvolume
0.47
0.61
0.48
0.65
Angle RMSD (*)
1.60
0.73
0.27
0.54
Ca deviations
0.09
0.00
0.00
0.00
Model Geometric
Ranachandran favored (%)1
95.48
96.33
98.03
99.68
Ramachandran outlier (%)
1.04
0.05
0.22
0.11
Metrics
Rotamer favored (%)f
96.80
80.99
97.43
98.58
Rotamer outlier (%)
1.14
1,48
0.87
0.51
F.5 RUNTIME PROFILING
To provide deeper insights into the computational efficiency of CryoNet we conducted detailed runtime profile analysis.
We profiled the exccution time of a single refinement recycle for a representative protein complex (e.g., BDBB-ksw, 1,900 residues). The breakdown of time consumption per iteration is detailed in Table
The results indicate that the Gradient Computation (Backpropagation) and the Loss Calculation the two primary computational bottlenecks. The forward pass of the diffusion model is relatively efficient due the one-step sampling.
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Published as a conference paper at ICLR 2026
Table 7: Runtime profile of single refinement recycle (averaged over total recycle).
Component
Time (ms)
Percentage (%)
Data Loading & Preprocessing
150
~66
Model Forward Pass (One-step)
200
77%
Loss Calculation (Density Geometry)
940
~355
Backpropagation Optimization
1420
~552
Total per Recycle
2710
100%
23


Reviews:
[{"review_id": "sKEw77KMkE", "reviewer": "Reviewer_9SBf", "summary": "This paper focuses on the process of fitting atomic models into experimental density maps for structure determination by cryo-electron microscopy (cryo-EM). Traditional refinement pipelines are computationally expensive and require extensive manual tuning. To address these challenges, the authors present CryoNet.Refine, an end-to-end deep learning framework that automates and accelerates molecular structure refinement. Specifically, CryoNet.Refine employs a one-step diffusion model that integrates a density-aware loss function with robust stereochemical restraints to rapidly optimize structures against experimental data. The framework is capable of refining not only protein complexes but also DNA/RNA–protein assemblies. Experimental results demonstrate that CryoNet.Refine achieves clear improvements over traditional approaches in both model–map correlation and overall geometric accuracy.", "questions": "1. If my assumption in Weakness 1 is correct, that no density or geometry loss is computed during inference, would it be beneficial to incorporate these losses as a form of test-time refinement? \n\n2. Figure 2 includes a Pairformer module, but it is never discussed in the text. Is this a Transformer-based component where cross-attention occurs between atom and sequence embeddings?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. This paper connects two important things in structural biology, computational modeling (e.g., AlphaFold3) and cryo-EM experimental density maps.\n\n2. The architecture design is well-motivated, improving efficiency while maintaining refinement quality.\n\n3. Presented experimental results demonstrate strong refinement performance, reduced manual effort, and clear efficiency gains over traditional methods.", "weaknesses": "1. It is confusing what exactly happens during a training step versus inference. I assume Fig. 2 provides an overview of the training process. During inference, there seems to be no computation of density or geometry loss, and the model likely performs only a single pass through the Atom Encoder, Sequence Embedder, and Diffusion Module. Clarifying this distinction would help readers better understand the workflow and computational efficiency.\n\n2. Several simple yet informative baselines are missing — for example, numerical optimization starting from the initial structure. Including such comparisons would better contextualize the claimed improvements.\n\n3. There is no ablation study comparing the classical diffusion model with the one-step diffusion approach. \n\n4. The density generator component is not evaluated. Details about its data patterns or visualizations are absent, and there is no discussion on how well the generated densities align with experimental cryo-EM maps, which can vary significantly depending on the instrument and imaging conditions.\n\n5. The number of reported test cases is too small. A larger-scale evaluation is necessary to establish robustness and generalizability across diverse molecular systems.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "6LgwVuSaLK", "reviewer": "Reviewer_6iZo", "summary": "This paper proposed a model for the refinement of atomic models based on CryoEM density map. Specifically, this work finetunes Boltz2 for each pair of density map and atomic model with the density loss and the geometry loss. The structure is output by a specially designed one-step diffusion module which enables direct back-propagation from the complex loss functions.", "questions": "- What would happen if we directly optimize the coordinates of the input structure instead of network parameters using the density loss and the geometry loss?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- The density loss is conceptually elegant and novel. The one-step diffusion module is well motivated as typical diffusion models can only be trained using specific loss function. The one-step diffusion allows flexible loss defitions.\n- Structure-specific post-training of the Boltz2 model ensures generalization. Previous works directly learn a mapping from density maps to atomic models, which might fail on structures that are significantly different from training data.\n- Better performance than previous methods.", "weaknesses": "- As it requires fine-tuning for each structure at inference time, the efficiency is still limited, and the efficiency improvement is not very significant compared to previous methods.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "WJajgefuOv", "reviewer": "Reviewer_aP6u", "summary": "CryoNet.Refine is an end-to-end framework that automates and accelerates molecular structure refinement. It utilizes a one-step diffusion model that integrates a density-aware loss function with robust stereochemical restraints, enabling it to rapidly optimize a structure against the experimental data.", "questions": "- In Section 3.1, line 193, the initial atomic structure is fed into CryoNet.Refine. You said that the model derived pair representation $z$ from the atomic structures. What is the shape of the pair representation? Is the side length of $z$ the number of residues, or the number of atoms?\n- I think AF3 can also benefit from the loss you proposed. What if adopting the loss you proposed to the predicted sample of AF3, like diffusion posterior sampling? (ref: (1) Diffusion posterior sampling for general noisy inverse problems, (2) CryoFM: a flow-based foundation model for cryoEM densities)\n- Since the model is initialzied from Boltz-2, why do you need some geometry loss to constrain the structures? I think a folding model has already contained such knowledge.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This study bridges the gap between structure prediction models and cryoEM densities in a modern approach. With some carefully designed loss functions, CryoNet.Refine brings the power of folding models to cryo-EM model building.\n- The ablation study is comprehensive, and the figures are well made.", "weaknesses": "- Why is the model named “one-step diffusion” but takes several recycling numbers?\n- The method part lacks several technical details, and is hard to follow. \n\t- What is the training set of CryoNet.Refine? Is it “trained” for each protein (like ReLION/CryoDRGN), or trained over a set of proteins and evaluated on some test set without tuning the model parameters?\n    - In Section 3.1, line 202, the authors wrote that the model is initialized from Boltz-2’s parameters.\n\t\t- Does CryoNet.Refine has exactly the same model architecture as Boltz-2?\n\t\t- If I am understanding correctly, CryoNet.Refine can be viewed as something like AF3 with classifier guidance. Is that true? \n\t- In line 208, the authors said that AF3 requires hundreds of sampling steps. In line 212, the authors wrote that one-step diffusion poses a key advantage that guidance can be performed directly on the predictions. I admit these two statements, but what confused me is that: AF3 is also a diffusion model which predicts the final sample (instead of predicting the velocity or noise), what is the difference between CryoNet.Refine and AF3?\n\t\t- Can I view AF3 as a one-step diffusion model, although it takes hundreds of steps in the sampling process?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "auF1KjgN95", "reviewer": "Reviewer_yjst", "summary": "This paper proposes CryoNet.Refine, a neural refinement framework that integrates a one-step diffusion model with experimental cryo-EM density map restraints.\nUnlike traditional refinement programs such as Phenix.real_space_refine, CryoNet.Refine introduces:\n1. A learnable density model that maps atomic coordinates to voxelized densities, enabling end-to-end differentiable correlation with experimental maps, and\n\n2. A geometry loss suite that includes differentiable Ramachandran, rotamer, and bond-length/angle penalties.\n\nThe model refines initial structures (often AlphaFold3 predictions) toward experimental densities, showing improvements in map correlation (CCmask, CCmain-chain) and stereochemical quality across 63 cryo-EM complexes.", "questions": "1. What concrete advantage does the diffusion step provide compared to standard coordinate optimization using the same losses?\n2. The authors state that they developed a novel, parameter-free, and differentiable density generator in the Introduction, but Section 3.2.1 indicates that they simply follow the ‘molmap’ implementation in ChimeraX. What, specifically, is novel in this component?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The combination of a density-aware differentiable loss and stereochemical constraints is technically sound.\n- The paper is well written\n- The paper demonstrates consistent gains over Phenix in both correlation coefficients and geometric metrics (notably, Ramachandran favored and rotamer outliers).", "weaknesses": "- The proposed “one-step diffusion” formulation is described as an innovation, but its necessity is not clearly demonstrated. The ablation shows marginal benefit, and it is unclear why a diffusion step—traditionally for generative sampling—improves deterministic refinement. A comparison to standard coordinate optimization (e.g., gradient descent using the same losses) would help establish that the diffusion mechanism contributes beyond architecture novelty.\n- The “density generator” is mentioned but not architecturally described (layers, parameters, training regime, loss balance weights γ). It is also unclear how the network differs from a Gaussian scattering baseline (molmap from ChimeraX).\n- The ablation in Table 4 shows individual loss terms but does not isolate the impact of the density model vs. geometry components.\nThe diffusion vs. non-diffusion refinement comparison (one-step vs. multi-step) is qualitative; quantitative runtime and accuracy tradeoffs are missing.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)