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Joint Discrete and SE(3) Diffusion for Protein Interface Design
Zhenqiao Song, Jianwen Xie, Lei Li
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
Last extracted: 10/14/2026, 10:19:36 AM
Summary
The paper introduces PIDiff, a multimodal diffusion framework for joint protein-protein complex design that co-designs binder sequences and structures conditioned on a target protein. PIDiff utilizes PIFormer, an architecture combining invariant point attention and sequence self-attention, to operate on discrete sequence space and continuous SE(3) structural manifolds. The authors also present PIBench, a large-scale dataset of protein-protein complexes, and demonstrate that PIDiff outperforms baselines in sequence design success rate, binding energy, and co-design consistency for minibinder and antibody design.
Entities (9)
Relation Signals (7)
PIDiff → trainedon → PIBench
confidence 100% · We first pretrain PIDiff on PIBench...
PIDiff → uses → PIFormer
confidence 100% · At its core, PIDiff employs PIFormer, a novel architecture...
PIDiff → appliedto → Antibody Design
confidence 90% · fine-tune it for ... antibody design.
PIDiff → appliedto → Minibinder Design
confidence 90% · fine-tune it for ... minibinder design
PIBench → derivedfrom → Protein Data Bank
confidence 90% · PIBench, a protein-protein complex dataset ... derived from the Protein Data Bank (PDB).
PIFormer → usesmechanism → Invariant Point Attention
confidence 90% · PIFormer ... interleaves geometry-aware invariant point attention...
PIFormer → usesinput → ESM-2
confidence 80% · incorporate pretrained residue representations extracted from ESM-2
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Abstract
Abstract:The design of high-affinity, target-specific protein binders is central to the development of modern therapeutics. However, existing protein-generation methods remain limited in this setting, as many generated designs fail to simultaneously achieve geometric and physicochemical complementarity at binding interfaces. To address this challenge, we introduce PIDiff, a physicochemically enhanced multimodal diffusion framework for protein-protein complex design. PIDiff jointly designs target-conditioned protein sequences and structures by coupling diffusion in discrete sequence space with diffusion on the continuous (SE(3)) structural manifold. At its core, PIDiff employs PIFormer, a novel architecture that interleaves geometry-aware invariant point attention with global sequence self-attention. We further curate PIBench, a protein-protein complex dataset with diverse target scaffolds derived from the Protein Data Bank (PDB). We first pretrain PIDiff on PIBench and subsequently fine-tune it for two therapeutically relevant applications: minibinder design and antibody design. PPFrame consistently outperforms baseline methods across sequence design success rate, structure binding energy, and sequence-structure co-designability on all tasks.
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- Source: https://arxiv.org/abs/2610.14699v1
- Canonical: https://arxiv.org/abs/2610.14699v1
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Joint Discrete and SE(3)SE(3) Diffusion for Protein Interface Design Zhenqiao Song Affiliation: Language Technologies Institute, Carnegie Mellon University Correspondence to: zhenqiaosong@cmu.edu Jianwen Xie Affiliation: Lambda Inc Lei Li Affiliation: Language Technologies Institute, Carnegie Mellon University Abstract The design of high-affinity, target-specific protein binders is central to the development of modern therapeutics. However, existing protein-generation methods remain limited in this setting, as many generated designs fail to simultaneously achieve geometric and physicochemical complementarity at binding interfaces. To address this challenge, we introduce PIDiff, a physicochemically enhanced multimodal diffusion framework for protein–protein complex design. PIDiff jointly designs target-conditioned protein sequences and structures by coupling diffusion in discrete sequence space with diffusion on the continuous SE(3)SE(3) structural manifold. At its core, PIDiff employs PIFormer, a novel architecture that interleaves geometry-aware invariant point attention with global sequence self-attention. We further curate PIBench, a protein–protein complex dataset with diverse target scaffolds derived from the Protein Data Bank (PDB). We first pretrain PIDiff on PIBench and subsequently fine-tune it for two therapeutically relevant applications: minibinder design and antibody design. PPFrame consistently outperforms baseline methods across sequence design success rate, structure binding energy, and sequence-structure co-designability on all tasks. Keywords: Machine Learning, ICML 1 Introduction The de novo design of high-affinity, target-specific protein binders is foundational to modern biomedicine, driving transformative advances in therapeutics (Nelson et al., 2010), diagnostics (Brennan et al., 2010), and vaccines (Correia et al., 2014; Sesterhenn et al., 2020). Central to molecular recognition is the requirement for strict geometric and physicochemical complementarity across the binding interface (Chothia and Janin, 1975; Conte et al., 1999; Gainza et al., 2023). The complementary interface is governed by core energetic drivers: van der Waals forces optimize spatial packing, while hydrophobic and electrostatic interactions enforce physicochemical compatibility. Although traditional methods have exploited these energetic principles to engage pre-selected surface patches (Chevalier et al., 2017; Silva et al., 2019), they frequently fail when target proteins lack well-defined binding pockets, thereby restricting their scope to a narrow range of target topologies. Recently, rapid advances in deep generative modeling have significantly expanded binder design capabilities (Evans et al., 2021; Cao et al., 2022; Bennett et al., 2023; Zambaldi et al., 2024; Stark et al., 2025; Sappington et al., 2026). These approaches have made it possible to design binders across diverse protein targets. In specialized domains, such as flexible peptides (Vázquez Torres et al., 2024) and intrinsically disordered proteins (Wu et al., 2024), deep generative models can yield potent binders without requiring extensive experimental optimization. Despite these breakthroughs, the overall success rate remains low due to two primary failure modes: the designed structure may fail to bind target interfaces due to the physicochemical or geometric non-complementarity, and the designed sequence may not fold into the intended structure. Crucially, most existing frameworks decouple sequence and structure generation or specialize in particular interaction types, leaving challenging, pocketless targets still intractable. To address these challenges, we present PIDiff, a physicochemically enhanced multimodal diffusion method to co-design binder protein sequence and structure for an arbitrary target. In our framework, proteins are represented as rigid-body frames, coupling each residue’s spatial backbone coordinates with its local physicochemical properties. PIDiff employs a unified multimodal diffusion process that operates jointly over discrete amino acid sequence space and the continuous SE(3)SE(3) structural manifold, progressively adding noise to train a joint generative model. The generative model is powered by PIFormer, an architecture that interleaves invariant point attention (Jumper et al., 2021) with sequence self-attention (Vaswani et al., 2017) to simultaneously capture spatial geometric constraints and amino acid dependencies. By tightly integrating sequence, structure, and physicochemical properties, PIDiff enforces binding interface complementarity and high sequence-structure consistency, effectively mitigating key failure modes in binder design to drive higher success rates. Concretely, our contributions are listed as follows: • We propose PIDiff, a multimodal diffusion method building upon PIFormer to co-design the binder protein sequences and structures for arbitrary protein targets. • We create PIBench, a general protein-protein complex dataset across diverse target geometries comprising 602,364 complexes curated from PDB (Berman et al., 2000). • Our model pretrained on PIBench outperforms strong baselines, demonstrating a sequence design success rate of 47.8%, structure binding energy of -67.8 and a co-design consistency of 65.2%. • We finetune the pretrained PIDiff on two important real-world applications: target-protein mini-binder complex design and antigen-antibody complex design. The finetuned models achieve design success rates of 40.7%40.7\% and 18.7%18.7\%, respectively, demonstrating the framework’s effectiveness in addressing key therapeutic challenges. 2 Related Work Protein-Protein Complex Design. Designing target-specific protein binders with high affinity has been extensively explored using a wide range of approaches. Conventional experimental approaches rely primarily on directed evolution of natural protein scaffolds (Vazquez-Lombardi et al., 2015) or high-throughput antibody screening from synthetic libraries (Chao et al., 2006; Hackel et al., 2008). Although powerful, these methods require considerable experimental effort and do not provide substantial control over the properties of the binder proteins. Traditional computational methods have sought to model physicochemical properties to accelerate the design process (Chevalier et al., 2017; Fleishman et al., 2011). However, their reliance on pre-defined hotspot residues heavily restricts their scope. Recent advances in deep learning have significantly improved the prediction and design of protein-protein interactions (Evans et al., 2021; Humphreys et al., 2021; Bryant et al., 2022; Pacesa et al., 2024; Didi et al., 2026), enabling binder design without prior hotspot specification (Cao et al., 2022; Bennett et al., 2023; Chen et al., 2025). Nevertheless, the overall success rate remains low due to the difficulty of simultaneously satisfying the strict geometric and physicochemical complementarity essential for stable physical binding interfaces (Berger et al., 2024; Zambaldi et al., 2024). Diffusion Models. Diffusion models (Sohl-Dickstein et al., 2015) have established themselves as a powerful class of generative frameworks. Ho et al. (2020) introduce denoising diffusion probabilistic models, formalizing their connection to score-based generative modeling (Song and Ermon, 2019). Diffusion models have achieved remarkable success in computational protein design. Early structural approaches focus on backbone design, progressing from CαC_α trace generation (Trippe et al., 2022) to full rigid-body SE(3)SE(3) backbone modeling (Watson et al., 2023; Yim et al., 2023). In parallel, discrete diffusion formulations are introduced to tackle protein sequence generation (Alamdari et al., 2023; Wang et al., 2024). More recent efforts have explored joint sequence-structure co-design through multimodal diffusion (Song et al., 2025; Wang et al., 2025). However, the application of diffusion models for the sequence-structure co-design of protein complexes still remains an open problem. 3 Proposed Method: PIDiff 3.1 Problem Definition We model a protein as a joint representation of its amino acid sequence and 3D backbone structure. Let A denote the set of 2020 standard amino acids. A protein of length L is represented by a sequence =a1,a2,…,aL∈L a=\a_1,a_2,...,a_L\ ^L and an associated backbone structure s. Following Jumper et al. (2021), the backbone geometry is parameterized by a collection of local rigid frames mapping from reference coordinates [N∗,Cα∗,C∗,O∗]∈ℝ4×3[N^*,C_α^*,C^*,O^*] ^4× 3 centered at Cα∗=(0,0,0)C_α^*=(0,0,0). Specifically, for residue i∈1,…,Li∈\1,…,L\, the mainchain heavy atom coordinates [Ni,Ci,(Cα)i][N_i,C_i,(C_α)_i] are represented by applying a rigid body transformation i∈SE(3) T_i∈ SE(3) to the reference frame: [Ni,Ci,(Cα)i]=i⋅[N∗,C∗,Cα∗][N_i,C_i,(C_α)_i]= T_i·[N^*,C^*,C_α^*]. Each frame i=(i,i) T_i=( r_i, x_i) comprises a rotation matrix i∈SO(3) r_i∈ SO(3) and a translation vector i∈ℝ3 x_i ^3, acting on a spatial coordinate ∈ℝ3 v ^3 via i⋅=i+i T_i· v= r_i v+ x_i. The full backbone structure is thus defined as =1⋅[N∗,C∗,Cα∗],…,L⋅[N∗,C∗,Cα∗] s=\ T_1·[N^*,C^*,C_α^*],…, T_L·[N^*,C^*,C_α^*]\, with backbone oxygen atoms positioned using the torsion angle ψ around the Cα–C_α--C bond. Furthermore, each residue i is assigned a physicochemical feature vector i=(yi,ci) f_i=(y_i,c_i) encoding its hydrophobicity yiy_i and charge cic_i, yielding a protein feature sequence =(1,2,…,L) f=( f_1, f_2,…, f_L). Given a target protein =,,T=\ a^T, s^T, f^T\ of length M, the objective of protein-protein complex co-design is to generate a binder protein ℬ=ℬ,ℬB=\ a^B, s^B\ of length N displaying complementary physicochemical and geometric properties to target T. This entails jointly sampling the binder sequence ℬ=a1ℬ,…,aNℬ a^B=\a_1^B,…,a_N^B\ and backbone transformations ℬ=1ℬ,…,Nℬ T^B=\ T_1^B,…, T_N^B\ with aligned physicochemical features ℬ f^B. Formally, we formulate this co-design task as learning a conditional generative model pθ(ℬ∣)p_θ(B ) parameterized by θ. Figure 1: Overview of the proposed PIDiff architecture. At each diffusion time step, the target protein structure is rendered in green, while the binder protein is shown in pink. 3.2 Overall Model Architecture The overall architecture of PIDiff is illustrated in Figure 1. PIDiff is a multimodal denoising diffusion probabilistic model (DDPM) (Ho et al., 2020) designed for joint generation of a binder’s primary sequence ℬ a^B and backbone structure ℬ s^B conditioned on a target protein T. The framework models a forward perturbation process q that corrupts data state ℬ0∼q(ℬ0∣)B_0 q(B_0 ) into noise ℬ∼qnoiseB_T q_noise over T steps, alongside a parameterized reverse generative process pθp_θ: q(ℬ1:∣ℬ0,)=∏t=1q(ℬt∣ℬt−1,)pθ(ℬ0:∣)=p(ℬ)∏t=1pθ(ℬt−1∣ℬt,) splitq(B_1:T _0,T)&=Π _t=1^Tq(B_t _t-1,T)\\ p_θ(B_0:T )&=p(B_T)Π _t=1^Tp_θ(B_t-1 _t,T) split (1) Each latent variable ℬt=(tℬ,tℬ)B_t=( a^B_t, s^B_t) represents a hybrid state spanning discrete amino acid categories and continuous SE(3)SE(3) transformations. Model parameters θ are optimized by maximizing the standard evidence lower bound on log-likelihood: ℒVLB=q[logpθ(ℬ0∣ℬ1,)−∑t=2KL[q(ℬt−1∣ℬt,ℬ0,)∥pθ(ℬt−1∣ℬt,)]⏟ℒt] splitL_VLB&=E_q [ p_θ(B_0 _1,T)\\ &-Σ _t=2^T KL [q(B_t-1 _t,B_0,T) p_θ(B_t-1 _t,T) ]_L_t ] split (2) By unifying discrete sequence transitions with continuous manifold diffusion, PIDiff enhances sequence-structure consistency throughout generative sampling. 3.3 PIDiff Diffusion Process We formulate the joint forward diffusion process of protein residue sequence tℬ a_t^B and backbone structure tℬ s^B_t as factorized transitions across individual residues and modalities at each time step t: q(ℬt∣ℬt−1,)=∏i=1Nq(ai,tℬ∣ai,t−1ℬ,)⋅∏i=1Nq(i,tℬ∣i,t−1ℬ,) splitq(B_t _t-1,T)&=Π _i=1^Nq(a^B_i,t a^B_i,t-1,T)\\ &·Π _i=1^Nq( s^B_i,t s^B_i,t-1,T) split (3) where ai,tℬa_i,t^B and i,tℬ=i,tℬ⋅[N∗,Cα∗,C∗] s_i,t^B= T_i,t^B·[N^*,C_α^*,C^*] denote the i-th residue type and local rigid frame at time step t, respectively. This factorization enables efficient noise sampling across different modalities. Discrete Sequence Diffusion. For the sequence components ℬ a^B, state transitions are defined via transition matrices [t]mn=q(ai,tℬ=n∣ai,t−1ℬ=m)[ Q_t]_mn=q(a^B_i,t=n a^B_i,t-1=m). Expressing ai,tℬa_i,t^B as a one-hot row vector i,tℬ a_i,t^B, the single-step transition is given by: q(i,tℬ∣i,t−1ℬ,)=Cat(i,tℬ,=i,t−1ℬt) q( a^B_i,t a^B_i,t-1,T)=Cat( a^B_i,t; p= a^B_i,t-1 Q_t) (4) where Cat(,)Cat( a; p) denotes a categorical distribution with probability vector p. Starting from i,0ℬ a^B_i,0, the t-step marginal and posterior distributions are analytically derived as: q(i,tℬ∣i,0ℬ,)=Cat(i,tℬ,=i,0ℬ¯t),¯t=∏j=1tjq(i,t−1ℬ|i,tℬ,i,0ℬ,)=Cat(i,t−1ℬ,=i,tℬt⊤⊙i,0ℬ¯t−1i,0ℬ¯ti,tℬ⊤) split&q( a^B_i,t a^B_i,0,T)=Cat( a^B_i,t; p= a^B_i,0 Q_t), 9.24994pt 9.24994pt Q_t=Π _j=1^t Q_j\\ &q( a^B_i,t-1| a^B_i,t, a^B_i,0,T)=Cat ( a^B_i,t-1; p= a^B_i,t Q_t a^B_i,0 Q_t-1 a^B_i,0 Q_t a^B _i,t )\\ split (5) Following Austin et al. (2021), we adopt an absorbing-state transition matrix t Q_t with an absorbing token [mask], where each token either remains unchanged or transitions to [mask] with probability βt _t: [t]mn=1if m=n=[mask]1−βtif m=n≠[mask]βtif n=[mask],m≠[mask] [ Q_t]_mn= cases1&if m=n=[mask]\\ 1- _t&if m=n≠[mask]\\ _t&if n=[mask],m≠[mask] cases (6) Continuous Structure Diffusion on SE(3)SE(3). To generate backbone structures in SE(3)NSE(3)^N, we build upon Riemannian score-based generative modeling (De Bortoli et al., 2022). Following Yim et al. (2023), we treat the rotational SO(3)SO(3) and translational ℝ3R^3 sub-manifolds independently, setting the final invariant distribution to pSE(3)(i,tℬ)∝SO(3)(i,tℬ)(i,tℬ,,3)p_SE(3)( T^B_i,t) _SO(3)( r^B_i,t)\,N( x^B_i,t;0, I_3). The forward Stochastic Differential Equation (SDE) on i,tℬ=(i,tℬ,i,tℬ) T^B_i,t=( r^B_i,t, x^B_i,t) is defined by: di,tℬ=[,−12i,tℬ]dt+[dSO(3)(i,t),dℝ3(i,t)] d T^B_i,t= [0,- 12 x^B_i,t ]dt+ [d B^(i,t)_SO(3),d B^(i,t)_R^3 ] (7) where SO(3) B_SO(3) and ℝ3 B_R^3 denote Brownian motions on SO(3)SO(3) and ℝ3R^3, respectively. The score network sθ(t,i,tℬ,)s_θ(t, T_i,t^B;T) is trained via denoising score matching: ℒstruct=[λt‖∇i,tℬlogpt|0(i,tℬ∣i,0ℬ;)−sθ(t,i,tℬ,)‖2] _struct=E [ _t \| _ T^B_i,t p_t 0( T^B_i,t T^B_i,0;T)-s_θ(t, T_i,t^B;T) \|^2 ] (8) By leveraging independence across coordinates, the conditional score decomposes into rotational and translational components: ∇i,tℬlogpt|0=[∇i,tℬlogpt|0,∇i,tℬlogpt|0] _ T^B_i,t p_t 0=[ _ r^B_i,t p_t 0,\, _ x^B_i,t p_t 0]. For SO(3)SO(3), the perturbation kernel pt|0p_t 0 is governed by the heat kernel on SO(3)SO(3) (Hsu, 2002), enabling analytical score evaluation: ∇i,tℬlogpt|0(i,tℬ∣i,0ℬ,)=i,tℬωi,tlog((i,0ℬ)⊤i,tℬ)∂ωf(ωi,t,t)f(ωi,t,t)f(ω,t)=∑l=0∞(2l+1)e−l(l+1)t/2sin((l+1/2)ω)sin(ω/2) split& _ r^B_i,t p_t 0( r^B_i,t r^B_i,0,T)= r^B_i,t _i,t (( r^B_i,0) r^B_i,t ) _ωf( _i,t,t)f( _i,t,t)\\ &f(ω,t)= _l=0^∞(2l+1)e^-l(l+1)t/2 ((l+1/2)ω) (ω/2) split (9) where ωi,t=ω((i,0ℬ)⊤i,tℬ) _i,t=ω(( r^B_i,0) r^B_i,t) is the rotation angle in radians. For ℝ3R^3, the translation process follows an Ornstein-Uhlenbeck process (Song et al., 2020) with kernel pt|0(i,tℬ∣i,0ℬ)=(i,tℬ;e−t/2i,0ℬ,(1−e−t)3)p_t 0( x^B_i,t x^B_i,0)=N( x^B_i,t;e^-t/2 x^B_i,0,(1-e^-t) I_3), yielding the exact conditional score: ∇i,tℬlogpt|0(i,tℬ∣i,0ℬ,)=(1−e−t)−1(e−t/2i,0ℬ−i,tℬ) _ x^B_i,t p_t 0( x^B_i,t x^B_i,0,T)=(1-e^-t)^-1 (e^-t/2 x^B_i,0- x^B_i,t ) (10) 3.4 PIFormer Architecture for the Reverse Generative Process The reverse generative process parameterizes the conditional transition distribution pθ(ℬt−1∣ℬt,)p_θ(B_t-1 _t,T) to reconstruct uncorrupted sequence-structure pairs from noisy states. We parameterize this reverse mapping using PIFormer, a multi-block neural architecture designed for joint sequence-structure co-design. PIFormer iteratively refines spatial frames and sequence representations across K stacked blocks. Each block interleaves spatial-based invariant point attention (IPA) layer (Jumper et al., 2021) with sequence-based self-attention layers, effectively modeling 3D geometric interactions alongside global amino acid dependencies. Node embeddings 0=(10,…,N^0)∈ℝN^×dh h^0=( h^0_1,…, h^0_ N) N× d_h are initialized with residue-level physicochemical features, while edge embeddings 0∈ℝN^×N^×dz z^0 N× N× d_z capture pairwise initial geometry following Trippe et al. (2022), where N^=M+N N=M+N denotes the total residue length of the target-binder complex. To enhance sequence modeling capacity, we incorporate pretrained residue representations ∈ℝN^×de e N× d_e extracted from ESM-2 (Lin et al., 2022). Within the l-th block (l∈1,…,Kl∈\1,…,K\), representations and rigid frames are updated as follows: (l−0.75) h^(l-0.75) =IPALayer((l−1),(l−1),(l−1)), =IPALayer ( h^(l-1), z^(l-1), T^(l-1) ), (11) (l−0.5) h^(l-0.5) =LayerNorm((l−0.75)+(l−1)) =LayerNorm ( h^(l-0.75)+ h^(l-1) ) (l−0.25) h^(l-0.25) =Transformer((l−0.5)+) =Transformer ( h^(l-0.5)+ e ) l h^l =LayerNorm(Linear((l−0.25))+(l−0.5)) =LayerNorm (Linear( h^(l-0.25))+ h^(l-0.5) ) ~l T^l =lf = h^l W_f l r^l =l−1+l−1⋅~l[:3],l=l−1+l−1⋅~l[3:] = r^l-1+ r^l-1· T^l_[:3], x^l= x^l-1+ r^l-1· T^l_[3:] l T^l =(l,l) =( r^l, x^l) l z^l =FFN(f(l,(l−1))) =FFN (f( h^l, z^(l-1)) ) fij(l,(l−1)) f_ij( h^l, z^(l-1)) =Concatenate(Linear(il),Linear(jl),ij(l−1)) =Concatenate (Linear( h^l_i),Linear( h^l_j), z^(l-1)_ij ) where f∈ℝdh×6 W_f ^d_h× 6 is a trainable projection matrix, and 0=[,~ℬ] T^0=[ T^T, T^B] concatenates ground-truth target frames T^T with perturbed binder frames ~ℬ T^B. FFN denotes the feed-forward layer. From the final outputs (K,K)( h^K, T^K), we compute rotational and translational scores, predict the uncorrupted sequence distribution, and estimate backbone ψ torsion angles: sθr,i=fr(~iℬ,iℬ,K),sθx,i=fx(~iℬ,iℬ,K)pθ(^i,0ℬ)=Softmax(Linear(iK)),ψi=fψ(iK) splits^r,i_θ&=f_r( r_i^B, r_i^B,K), 9.24994pts^x,i_θ=f_x( x_i^B, x_i^B,K)\\ p_θ( a_i,0^B)&=Softmax (Linear( h_i^K) ), 9.24994pt _i=f_ψ( h_i^K) split (12) where frf_r and fxf_x compute score function approximations from noisy frames (~iℬ,~iℬ)( r_i^B, x_i^B) and network-predicted frames (iℬ,K,iℬ,K)( r_i^B,K, x_i^B,K), and fψf_ψ maps node representations to ψ torsion angles. The predicted distribution pθ(^i,0ℬ)p_θ( a_i,0^B) parameterizes the clean sequence i,0ℬ a_i,0^B, allowing analytical calculation of the reverse categorical posterior pθ(i,t−1ℬ|i,tℬ,^i,0ℬ,)p_θ( a^B_i,t-1| a^B_i,t, a^B_i,0,T). 3.5 Training Objective To achieve effective sequence-structure co-design, PIDiff is optimized via a multitask learning objective ℒtL_t that combines discrete sequence learning, continuous SE(3)SE(3) score-matching frame losses, and late-stage auxiliary physical regularization with weights α, γ, and ω: ℒt=αℒseq+γ(ℒstructr+ℒstructx)+ωℒauxℒseq=∑i=1NKL(q(ℬi,t−1∣ℬi,t,ℬi,0,)∥pθ(ℬi,t−1|ℬi,t,^ℬi,0,))ℒstructr=∑i=1N‖∇i,tℬlogpt|0(i,tℬ∣i,0ℬ,)−sθr,i‖2,ℒstructx=∑i=1N‖iℬ−iℬ,K‖2 splitL_t&= _seq+γ(L_struct^r+L_struct^x)+ _aux\\ L_seq&=Σ _i=1^NKL (q( a^B_i,t-1 a^B_i,t, a^B_i,0,T)\; \;p_θ( a^B_i,t-1| a^B_i,t, a^B_i,0,T) )\\ L_struct^r&=Σ _i=1^N \| _ r_i,t^B p_t 0( r_i,t^B r_i,0^B,T)-s_θ^r,i \|^2,\\ L_struct^x&=Σ _i=1^N \| x_i^B- x_i^B,K \|^2 split (13) where ℒseqL_seq maximizes the variational lower bound in Eq. 2, and the frame losses minimize the score-matching objective in Eq. 8. By applying target weighting schedules λi,tr=1/[‖∇logpt|0(i,t∣i,0)‖SO(3)2] _i,t^r=1/E [\|∇ p_t 0( r_i,t r_i,0)\|_SO(3)^2 ] for rotations and λi,tx=(1−e−t)/e−t/2 _i,t^x=(1-e^-t)/e^-t/2 for translations, the frame objectives simplify to the unweighted formulations above. To enforce physical contact fidelity during final structure generation, we activate two auxiliary terms, ℒaux=ℒstructatom+ℒstructpairL_aux=L_struct^atom+L_struct^pair, during late denoising time steps (t<0.25t<0.25): ℒstructatom _struct^atom =14N∑i=1N∑m∈‖i,mℬ−i,mℬ,K‖2,=N,Cα,C,O = 14N _i=1^N _m \| x_i,m^B- x^B,K_i,m \|^2, 9.24994ptA=\N,C_α,C,O\ (14) ℒstructpair _struct^pair =1S∑1≤i≠j≤N∑m,n∈(dmnij<τ)‖dmnij−d^mnij‖2 = 1S _1≤ i≠ j≤ N _m,n I(d^ij_mn<τ) \|d^ij_mn- d^ij_mn \|^2 S S =∑1≤i≠j≤N∑m,n∈(dmnij<τ) = _1≤ i≠ j≤ N _m,n I(d^ij_mn<τ) where d∗d^* denotes the pairwise atomic distances, and τ specifies the interaction distance cutoff. 3.6 Self-Conditioned Inference During inference, conditioned on the target protein’s sequence a^T, structure s^T, and physicochemical features f^T, PIDiff conditionally co-samples the binder sequence ℬ a^B and backbone structure ℬ s^B to yield high-affinity complexes. Sequence generation initializes all binder positions in an absorbing state [mask], fixing residue types and updating physicochemical features ℬ f^B upon state transition. Structure generation utilizes Euler-Maruyama geodesic random walks on SE(3)SE(3) over T steps (De Bortoli et al., 2022). Translations receive Gaussian updates from (,3)N(0, I_3), while rotations update along the Lie algebra SO(3)SO(3) tangent space as i,t′=i,t∑j=13δjj r _i,t= r_i,t _j=1^3 _j e_j with δj∼i.i.d.(0,1) _j .i.d. N(0,1) and 1,2,3 e_1, e_2, e_3 are orthonormal basis vectors. To maximize structural fidelity, we implement a self-conditioned inference scheme at each time step t: PIFormer first performs an intermediate forward pass to update CαC_α positions, then recalculates spatial pair embeddings to refine sequence likelihoods and rigid frames in a second pass. 4 Experiments Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.523 81.61 21.73% 37.90% 73.01% -45.97 50.00% 50.00% APM 0.252 77.66 2.17% 31.26% 53.27% -45.12 23.91% 34.78% Complexa 0.521 84.61 30.43% 53.77% 82.69% -56.57 56.52% 54.34% PIDiff 0.592 87.18 47.83% 33.22% 57.49% -67.80 65.22% 65.22% Table 1: Model performance on general protein-protein complex design task. Our PIDiff achieves the best sequence design success rate, structure binding energy and sequence-structure co-designability. 4.1 PIBench Construction To establish a foundation model for protein-protein complex design that can be seamlessly adapted to real-world applications, we curate a comprehensive dataset called PIBench. Following the data processing pipeline of AlphaFold3 (Abramson et al., 2024), we extract 301,182 chain-pair interfaces from the PDB. Complete processing workflows are detailed in Appendix A.1. By treating both chains within each interface symmetrically as target-binder pairs, we construct a benchmark comprising 602,364 complexes across diverse scaffolds. To prevent data leakage, sequences are clustered at 50% identity, yielding 28,884 distinct clusters. We reserve 10 clusters each for validation and testing, allocating the remaining clusters for training. Detailed data statistics are given in Appendix Table 4. 4.2 Experimental Setup Implementation Details. The PIFormer comprises five blocks, each containing one IPA layer and six self-attention layers. Parameters for the self-attention layers are initialized from the pretrained 150M ESM-2 model. Node and edge embedding dimensions are set to 640 and 320, respectively, bringing the total parameter count of PIDiff to 240M. The diffusion process is configured for 1,000 steps. In inference, for each target protein, we generate 10 binder candidates and rank them by their complex pLDDT scores, selecting the top-k candidates. More implementation details are provided in Appendix B. Baseline Models. We compare the proposed PIDiff against the following representative protein complex co-design methods: (1) RFD+ProteinMPNN (IF) first applies RFDiffusion (Watson et al., 2023) to design a binder protein structure based on the given target and then uses ProteinMPNN (Dauparas et al., 2022) to generate the corresponding sequence. (2) APM (Chen et al., 2025) is an all-atom generative model for protein complex design. (3) Proteína-Complexa (Didi et al., 2026) is a fully atomistic binder generation method showing strong performance on protein-binding protein design. Evaluation Metrics. To comprehensively evaluate PIDiff, we assess generated complexes across three dimensions: sequence quality, structure reliability, and sequence-structure consistency. Sequence Evaluation: We evaluate designed sequences using five metrics: (1) ipTM via AlphaFold3 (AF3) to measure interface confidence; (2) pLDDT via AF3 to assess complex structure stability; (3) Success Rate (SR) defined as the fraction of designed candidates that simultaneously achieve an ipTM>0.8ipTM>0.8 and a pLDDT>80pLDDT>80; (4) Diversity, measured as the amino acid variation among candidates for the same target; and (5) Novelty, calculated as the sequence dissimilarity between candidates and reference sequences. Structure Evaluation: We assess designed structures via: (6) Binding Energy (ΔG G), computed via Rosetta (Chaudhury et al., 2010) to estimate interface energetic stability, where lower values indicate stronger binding propensity, and (7) Designability, defined as the fraction of designs achieving a self-consistency RMSD (scRMSDscRMSD) <2Å<2\, (Trippe et al., 2022). Sequence-Structure Consistency: We measure joint consistency via (8) Co-designability (Consistency), defined as the proportion of generated binder sequences whose AF3-folded structure matches the corresponding designed structures within 2Å2\, RMSD (Didi et al., 2026). Models FGFR2 (Seen) InsulinR (Seen) PDGFR (Seen) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) RFD+IF 36.84% -42.04 63.15% 56.52% -35.35 65.21% 3.84% -59.37 53.84% APM 29.82% -37.02 54.38% 43.47% -31.04 82.61% 0.0 -61.54 61.53% Complexa 54.38% -45.81 73.68% 78.26% -41.32 86.95% 19.23% -66.56 88.46% PIDiff 61.40% -50.87 98.24% 86.95% -46.92 100% 7.69% -68.82 30.76% Models TGFb (Seen) VirB8 (Seen) EGFR (Zero-shot) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) RFD+IF 11.11% -31.09 55.56% 14.28% -32.91 57.14% 25.00% -46.87 25.00% APM 11.11% -23.16 11.11% 0.0 -19.59 42.85% 0.0 -32.76 50.00% Complexa 22.22% -46.54 33.33% 14.28% -38.56 85.71% 0.0 -40.90 50.00% PIDiff 22.22% -49.29 22.22% 14.28% -48.31 100% 0.0 -48.35 100.0% Models H3 (Zero-shot) IL7Ra (Zero-shot) Tie2 (Zero-shot) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) RFD+IF 52.63% -35.93 26.31% 14.28% -40.08 42.85% 50.00% -38.95 75.00% APM 47.38% -36.45 42.10% 0.0 -23.93 57.14% 0.0 -27.85 50.00% Complexa 60.52% -40.65 47.36% 28.57% -42.26 71.42% 0.0 -33.83 50.00% PIDiff 97.36% -47.08 31.57% 42.85% -50.42 100% 0.0 -42.39 100.00% Models TrkA (Zero-shot) Average Novelty (↑ ) Diversity (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) RFD+IF 25.00% -33.28 50.00% 28.95% -39.59 51.41% 70.69% 30.38% APM 25.00% -31.92 25.00% 15.67% -32.53 47.67% 51.47% 29.02% Complexa 50.00% -41.50 50.00% 32.74% -43.79 63.69% 78.69% 42.69% PIDiff 75.00% -46.04 75.00% 40.77% -49.85 75.78% 81.24% 29.08% Table 2: Model performance on target-protein mini-binder complex design task. Consistency denotes sequence-structure co-designability. Our PIDiff achieves the best average sequence design success rate, structure binding energy and sequence-structure co-designability. 4.3 General Protein-Protein Complex Design This task evaluates the foundational capability of PIDiff to design protein-protein complexes across diverse target scaffolds. We train and evaluate PIDiff on our curated PIBench. Top-1 candidate performance for all methods is summarized in Table 1. PIDiff demonstrates the best performance in generating high-affinity, structurally consistent binders across a wide spectrum of targets. Specifically, PIDiff achieves top performance across all metrics spanning sequence quality, structural reliability, and sequence-structure co-designability, reaching a sequence design success rate of 47.83%, an interface binding energy of −67.8-67.8, and a co-designability score of 65.22%. Although sequence diversity and novelty scores are slightly lower than those of Proteína-Complexa, PIDiff achieves higher structural diversity (Appendix Table 7). This indicates that PIDiff successfully generates binders with flexible loop configurations and distinct subdomain topologies, whereas binders from Proteína-Complexa have almost invariant secondary structure cores. 4.4 Target Protein-Mini Binder Complex Design Datasets. We curate experimentally validated target-protein mini-binder complexes across ten diverse target classes from Bennett et al. (2023). For targets with more than 50 complexes, we partition the data using a random 8:1:1 train/validation/test split. For targets with fewer complexes, all instances are reserved for testing to evaluate model generalization in a zero-shot setting. Comprehensive dataset statistics are provided in Appendix Table 5. Main Results. The results for target-protein mini-binder complex design are summarized in Table 2, with target-specific breakdowns provided in Appendix Tables 8–17. Overall, PIDiff demonstrates superior capacity for generating novel, high-affinity binders across diverse target classes. Specifically, PIDiff achieves higher sequence design success rates on 7 out of 10 targets, superior structure binding energy across all 10 targets, and improved co-designability on 7 out of 10 targets. Notably, PIDiff also yields higher novelty scores, reversing the trend observed in our general complex design task. We attribute this shift to the distinctions between the fine-tuning dataset and PIBench, enabling PIDiff to navigate a broader candidate space for novel binder discovery. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) H1-Novelty (↑ ) H2-Novelty (↑ ) H3-Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.508 80.05 16.79% 47.30% 56.22% 61.98% -33.09 59.29% 59.29% APM 0.256 77.92 6.61% 45.71% 54.17% 64.43% -26.68 53.57% 52.74% Complexa 0.515 81.08 16.92% 53.80% 66.26% 71.91% -32.80 90.26% 92.32% PIDiff 0.526 81.41 18.77% 52.31% 67.85% 71.93% -44.46 98.34% 99.39% Table 3: Model performance on antigen-antibody complex design task. Our PIDiff achieves the best sequence design success rate, structure binding energy and sequence-structure co-designability. 4.5 Antigen-Antibody Complex Design Dataset. Following Jin et al. (2022), we curate 4,2614,261 complete antigen-antibody complexes from the Structural Antibody Database (Dunbar et al. (2014), SAbDab) by removing cases lacking a light chain or antigen. Train/validation/test splits (8:1:1 ratio) are constructed by clustering individual CDR sequences at 40% identity using MMseqs2 (Steinegger and Söding, 2017), yielding 1,034 (CDR-H1), 1,418 (CDR-H2), and 2,254 (CDR-H3) clusters. Full split statistics are provided in Appendix Table 6. Main Results. Average performance across distinct CDR cluster splits for antigen-antibody complex design is summarized in Table 3, with CDR-specific breakdowns detailed in Appendix Tables 18–20. Overall, PIDiff outperforms all baselines in generating high-affinity and novel antibodies. Specifically, PIDiff achieves top performance across sequence design success rate, CDR H2/H3 novelty, interface binding energy (ΔG G), and sequence-structure co-designability. Crucially, both the designability and co-designability of PIDiff exceed 95%95\%, demonstrating exceptional structure fidelity and tight sequence-structure consistency. (a) Model Scaling (b) Physicochemical Properties (c) Self-Consistency (d) Structure Learning (e) Binder Finetuning (f) General Protein Complex (g) Binder Design (h) Antibody Design Figure 2: Ablation study: (a) - (e), and case study with target protein (f) PDB 1STX.E, (g) InsulinR, (h) HIV-1 (7UCG). Target proteins are shown in blue, the folded structures for the designed binder sequences in green, and the designed binder structures in gray, with light chain in pink for antibody. 5 Analysis 5.1 Does Model Scale Help? PIDiff scales effectively with parameter capacity. We benchmark our 240M PIDiff against a smaller model (76M) configured with 4 blocks and a hidden dimension of 480. As shown in Figure 2(a), scaling capacity improves sequence success rate, structural designability, and co-designability on PIBench. These results highlight the scalability of our architecture, indicating that performance scales predictably with model capacity. 5.2 Effect of Physicochemical Complementarity Constraints As stable protein-protein interactions depend on complementary geometries and physicochemical properties, we conduct an ablation study by training a variant of PIDiff without physicochemical features on PIBench. As illustrated in Figure 2(b), omitting these constraints leads to a significant performance degradation across both sequence and structural metrics. These findings confirm that explicitly incorporating physicochemical features is critical for stable interface design. 5.3 Influence of Self-Consistency To evaluate the role of self-consistency during inference, we conduct an ablation by disabling this mechanism on the general protein-protein complex design task. As shown in Figure 2(c), removing self-consistency yields a measurable drop in both structural designability and co-designability. This validates self-consistency as an effective inference-time strategy for generating reliable structures and reinforcing sequence-structure co-design alignment. 5.4 Impact of Joint Co-Design and Auxiliary Losses To isolate the contributions of the joint sequence-structure co-design mechanism and auxiliary supervision, we evaluate a structure-only ablation (PIDiff w/o seq) alongside a model variant trained without auxiliary loss terms (PIDiff w/o auxiliary loss). As illustrated in Figure 2(d), both components enhance structural designability, with sequence-structure co-design exerting a significantly stronger effect. We attribute these gains to the stricter physical regularization provided by both mechanisms, confirming that they are vital for designing reliable structures. 5.5 Impact of Supervised Fine-Tuning To evaluate how domain-specific adaptation affects downstream performance, we compare our pretrained PIDiff on the mini-binder design task. As shown in Figure 2(e), targeted fine-tuning improves interface binding energy (ΔG G) across 6 out of 10 targets, slightly promoting the mean energy score from −48.98-48.98 to −49.85-49.85. Full results are provided in Appendix Table 21. These results demonstrate that while our pretrained model already possesses robust zero-shot design capabilities, supervised fine-tuning further enhances binding affinity for specialized applications. 5.6 Designing Diverse and High-Affinity Protein Complexes Figures 2(f)–(h) showcase qualitative case studies across general complex, mini-binder, and antibody design tasks. Spanning distinct target topologies, the generated candidates consistently satisfy stringent quality thresholds: ipTM >0.8>0.8, pLDDT >85>85, interface binding energy <−35<-35, and co-design RMSD <2Å<2\, . This highlights PIDiff’s ability to co-design highly consistent binder sequences and structures against diverse target scaffolds. 6 Conclusion In this work, we introduce PIDiff, a physicochemically enhanced multimodal diffusion method for joint binder protein sequence-structure co-design. Powered by PIFormer, an architecture combining IPA layer with sequence-level self-attention, PIDiff effectively couples 3D geometry with amino acid dependencies. Across general protein complex generation as well as specialized mini-binder and antibody design tasks, PIDiff consistently surpasses state-of-the-art baselines across multiple metrics. Overall, PIDiff demonstrates strong potential as a robust and scalable tool for computational binder discovery. A potential limitation is the absence of wet-lab validation, which is an essential step planned for our future research to further validate the model’s practical utility. References Abramson et al. (2024) J. Abramson, J. Adler, J. Dunger, R. 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The curation process begins by applying a series of quality filters to identify valid PDB entries: • Retain structures with a reported resolution of 9Å or better. • Remove polymer chains containing unknown residues. • Exclude protein chains where consecutive CαC_α atoms are separated by more than 10Å. • Filter out polymer chains with fewer than four resolved residues. • Eliminate clashing chains, defined as chains with more than 30% of their atoms located within 1.7Å of an atom in another chain. When two chains clashed: – The chain with the higher percentage of clashing atoms is removed. – If the clashing percentage is equal, the chain with fewer total atoms is removed. – If both chains have the same number of atoms, the chain with the larger chain ID is removed. This filtering process result in 68,891 valid PDB entries. From these entries, chain-pair interfaces are identified, defined as pairs of chains with a minimum heavy atom separation of less than 5Å. Furthermore, to ensure efficient processing, all complexes are filtered to exclude sequences longer than 1,024 residues, finally resulting in a total of 301,182 chain-pair interfaces. A.2 PIBench Data Statistics Complex Training 602,129 Validation 189 Test 46 Total 602,364 Table 4: Data statistics for PIBench. We provide the data statistics for the curated PIBench in Table 4. A.3 Data Statistics for Target-Protein Mini-Binder Complex Dataset Models Seen Class Zero-Shot FGFR2 InsulinR PDGFR TGFb VirB8 H3 IL7Ra EGFR TrkA Tie2 Training 465 192 210 77 57 – – – – – Validation 57 23 26 9 7 – – – – – Test 57 23 26 9 7 38 7 4 4 2 Total 579 238 262 95 71 38 7 4 4 2 Table 5: Detailed data statistics for curated target-protein mini-binder complex dataset. We collect experimentally confirmed positive target-protein mini-binder complexes against ten targets with diverse structural properties from Bennett et al. (2023). The detailed data statistics for the ten target proteins are reported in Table 5. A.4 Data Statistics for Antigen-Antibody Complex Dataset CDR-H1 Clustering CDR-H2 Clustering CDR-H3 Clustering Complexes 4,261 4,261 4261 Clusters 1,034 1,418 2,254 Training 3,590 3,576 3,427 Validation 403 399 451 Test 268 286 383 Table 6: Detailed data statistics for antigen-antibody complex dataset. We detail the data statistics of antigen-antibody complex dataset for each CDR clustering in Table 6. Appendix B Supplementary Implementation Details Diffusion Schedules. Continuous spatial noise scheduling is parameterized across both Euclidean and rotational manifolds. For translation vectors in ℝ3R^3, the variance schedule scales from σmin=0.1 _ =0.1 to σmax=20.0 _ =20.0. We use a coordinate scaling factor of 0.1. For rotation matrices in SO(3)SO(3), the schedule scales from σmin=0.1 _ =0.1 to σmax=1.5 _ =1.5. Architecture & Hyperparameters. The Invariant Point Attention (IPA) modules are configured with 88 attention heads, utilizing 88 query/key points and 1212 value points per head. Loss hyper-parameters are set to α=1.0α=1.0, γ=1.0γ=1.0, and ω=0.25ω=0.25, and the threshold τ for the pairwise distance constraint is set to 0.250.25. Training Setup. We train PIDiff on a single NVIDIA B200 GPU for up to 1.21.2 million steps. Optimization is performed with a learning rate of 11e−4-4 and a batch capacity of 1,5361,536 tokens per step. Validation is executed per 5,0005,000 gradient steps. Appendix C Supplementary Experimental Results C.1 Structure Diversity on the General Protein-Protein Complex Design Task Structure Diversity (↑ ) RFD+ProteinMPNN 0.3097 APM 0.3063 Proteína-Complexa 0.1597 PIDiff 0.3135 Table 7: Structure diversity on the general protein-protein complex design task, which is quantified as 1−TM-score1-TM -score averaged across generated candidate structures. Structural design diversity is quantified as 1−TM-score1-TM -score averaged across generated candidate structures. We interpret these diversity scores across three regimes: values above 0.50.5 represent high overall structural diversity; scores between 0.30.3 and 0.50.5 correspond to structures within the same superfamily that feature distinct loop configurations or subdomain topologies; and scores below 0.30.3 denote closely related structures sharing nearly identical secondary structure cores. As reported in Table 7, PIDiff achieves the highest structural diversity score, demonstrating a capacity to sample diverse loop structures and topological variations rather than collapsing onto rigid backbone templates. C.2 Detailed Target-Protein Mini-Binder Complex Design Results The detailed target-protein mini-binder complex design results for different targets are provided in Table 8 - 17. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.637 78.92 36.84% 31.97% 68.25% -42.04 63.15% 63.15% APM 0.538 76.39 29.82% 29.05% 48.39% -37.02 71.92% 54.38% Complexa 0.823 80.67 54.38% 49.25% 76.91% -45.81 91.22% 73.68% PIDiff 0.931 82.58 61.40% 41.75% 77.74% -50.87 100% 98.24% Table 8: Model performance on target-protein mini-binder complex design for target FGFR2. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves the best performance across sequence evaluation, structural evaluation and sequence-structure consistency metrics. Additionally, PIDiff also obtains the highest novelty score. Altogether, the results validate PIDiff is capable of designing high-affinity and novel protein complexes. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.789 80.43 56.52% 30.89% 69.18% -35.35 65.21% 65.21% APM 0.562 79.01 43.47% 26.91% 52.91% -31.04 78.26% 82.61% Complexa 0.832 86.90 78.26% 41.93% 76.93% -41.32 100% 86.95% PIDiff 0.895 93.04 86.95% 27.54% 79.51% -46.92 100% 100% Table 9: Model performance on target-protein mini-binder complex design for target InsulinR. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves the highest sequence design success rate, structure binding energy and sequence-structure co-designability, validating its ability in simultaneously designing high-quality and consistent protein-protein complex sequences and structures. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.598 76.56 3.84% 28.93% 72.83% -59.37 53.84% 53.84% APM 0.391 73.89 0.0 30.27% 52.19% -61.54 65.38% 61.53% Complexa 0.652 78.09 19.23% 41.25% 79.42% -66.56 88.46% 88.46% PIDiff 0.678 81.73 7.69% 25.78% 82.43% -68.82 100% 30.76% Table 10: Model performance on target-protein mini-binder complex design for target PDGFR. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves better structure design performance, but lags behind Proteína-Complexa on both sequence design quality and sequence-structure design consistency. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.589 76.90 11.11% 35.17% 68.23% -31.09 55.56% 55.56% APM 0.461 72.10 11.11% 32.81% 48.65% -23.16 77.78% 11.11% Complexa 0.683 80.15 22.22% 46.17% 76.12% -46.54 88.89% 33.33% PIDiff 0.733 78.17 22.22% 48.57% 76.46% -49.29 100% 22.22% Table 11: Model performance on target-protein mini-binder complex design for target TGFb. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves better performance on both sequence and structure design quality. However, the sequence-structure co-designability of PIDiff is a bit lower than that of Proteína-Complexa. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.570 82.89 14.28% 32.95% 72.91% -32.90 57.14% 57.14% APM 0.368 85.09 0.0 30.19% 52.87% -19.59 71.74% 42.85% Complexa 0.602 86.10 14.28% 46.52% 80.15% -38.56 85.71% 85.71% PIDiff 0.657 86.67 14.28% 36.17% 81.16% -48.31 100% 100% Table 12: Model performance on target-protein mini-binder complex design for target VirB8. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff obtains better sequence and structure design quality as well as sequence-structure consistency. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.571 83.09 25.00% 29.15% 71.26% -46.87 25.00% 25.00% APM 0.512 83.19 0.0 27.93% 51.34% -32.76 50.00% 50.00% Complexa 0.627 86.76 0.0 40.16% 76.31% -40.90 100% 50.00% PIDiff 0.680 90.19 0.0 22.62% 82.56% -48.35 100% 100% Table 13: Model performance on target-protein mini-binder complex design for target EGFR. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves better structure binding energy and sequence-structure co-designability. However, the sequence design success rate of PIDiff is zero, which might be due to the lack of deep pockets of EGFR targets and the zero-shot setting of this class. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.782 78.56 52.63% 28.16% 71.04% -35.93 26.31% 26.31% APM 0.562 76.29 47.38% 23.91% 53.16% -36.45 49.87% 42.10% Complexa 0.891 79.05 60.52% 38.16% 80.47% -40.65 78.93% 47.36% PIDiff 0.934 82.32 97.36% 21.97% 83.16% -47.08 100% 31.57% Table 14: Model performance on target-protein mini-binder complex design for target H3. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff obtains higher sequence design success rate and lower structure binding energy, confirming that PIDiff has the capability to design high-affinity binders even in zero-shot setting. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.543 85.67 14.28% 29.18% 70.19% -40.08 42.85% 42.85% APM 0.429 78.09 0.0 27.56% 53.96% -23.93 85.71% 57.14% Complexa 0.634 89.90 28.57% 36.17% 80.16% -42.26 100% 71.42% PIDiff 0.734 92.21 42.85% 20.35% 82.30% -50.42 100% 100% Table 15: Model performance on target-protein mini-binder complex design for target IL7Ra. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves higher sequence design success rate, lower structure binding energy and higher sequence-structure co-designability. Note that the designability and co-designability of PIDiff on this target are both 100%, validating the strong binder design capability of PIDiff in the zero-shot setting. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.562 86.90 50.00% 29.31% 72.91% -38.95 75.00% 75.00% APM 0.421 82.19 0.0 30.19% 51.43% -27.85 100% 50.00% Complexa 0.590 90.10 0.0 39.42% 81.58% -33.83 100% 50.00% PIDiff 0.635 92.98 0.0 10.52% 88.20% -42.39 100% 100% Table 16: Model performance on target-protein mini-binder complex design for target Tie2. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). PIDiff achieves higher structure design quality and sequence-structure consistency. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) Diversity (↑ ) Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.791 72.08 25.00% 28.17% 70.16% -33.28 50.00% 50.00% APM 0.563 73.90 25.00% 31.42% 49.87% -31.92 75.00% 25.00% Complexa 0.829 80.10 50.00% 47.92% 78.93% -41.50 100% 50.00% PIDiff 0.840 80.31 75.00% 35.49% 78.92% -46.04 100% 75.00% Table 17: Model performance on target-protein mini-binder complex design for target TrkA. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). Similarly, PIDiff achieves better sequence design success rate, structure binding energy and sequence-structure consistency, confirming its ability in designing good binders in the zero-shot setting. C.3 Detailed Antigen-Antibody Complex Design Results for Each CDR Clustering We provide the detailed results of antigen-antibody complex design for each CDR clustering in Table 18 - 20. Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) H1-Novelty (↑ ) H2-Novelty (↑ ) H3-Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.538 80.67 15.67% 49.78% 51.26% 59.31% -30.03 58.20% 58.20% APM 0.239 79.23 7.46% 42.18% 53.37% 63.17% -29.38 57.08% 52.61% Complexa 0.523 81.09 14.92% 55.36% 68.26% 72.93% -35.35 88.43% 90.67% PIDiff 0.548 82.10 17.16% 56.64% 66.46% 74.68% -42.49 100% 100% Table 18: Model performance on antigen-antibody complex design task for CDR-H1 clustering. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) H1-Novelty (↑ ) H2-Novelty (↑ ) H3-Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.497 79.29 17.48% 43.87% 58.69% 62.89% -32.98 58.04% 58.04% APM 0.271 76.32 5.59% 45.28% 52.97% 63.16% -28.78 52.98% 53.14% Complexa 0.519 81.90 17.83% 52.79% 65.23% 70.95% -30.13 91.25% 93.35% PIDiff 0.506 80.62 19.58% 49.38% 67.21% 69.61% -44.37 100% 100% Table 19: Model performance on antigen-antibody complex design task for CDR-H2 clustering. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). Models Sequence Structure Co-designability (↑ ) ipTM (↑ ) pLDDT (↑ ) SR (↑ ) H1-Novelty (↑ ) H2-Novelty (↑ ) H3-Novelty (↑ ) Δ (↓ ) Designability (↑ ) RFD+IF 0.487 80.17 17.23% 48.26% 58.73% 63.75% -36.25 61.62% 61.62% APM 0.259 78.23 6.78% 49.67% 56.19% 66.97% -21.89 50.65% 52.48% Complexa 0.502 80.26 18.01% 53.26% 65.29% 71.86% -32.90 91.12% 92.95% PIDiff 0.525 81.50 19.58% 50.88% 69.85% 71.51% -46.53 95.03% 98.17% Table 20: Model performance on antigen-antibody complex design task for CDR-H3 clustering. (↑ ): the higher the better. (↓ ): the lower the better. IF denotes the inverse folding model ProteinMPNN (Dauparas et al., 2022) and Complexa denotes Proteína-Complexa (Didi et al., 2026). C.4 Detailed Binder Design Performance on the Pretrained Model Performance metrics for the pretrained PIDiff on target-protein mini-binder complex design are presented in Table 21. Notably, even without domain-specific adaptation, PIDiff exhibits robust zero-shot capabilities across diverse targets, most prominently in sequence-structure consistency, where it achieves 100%100\% co-designability across all evaluated targets. Subsequent supervised fine-tuning on a curated mini-binder dataset further elevates overall design quality, markedly boosting the mean sequence design success rate from 8.72%8.72\% to 40.77%40.77\%. These results confirm that while pretraining imparts strong zero-shot structural alignment, targeted fine-tuning substantially enhances sequence-level binding optimization. Models FGFR2 (Seen) InsulinR (Seen) PDGFR (Seen) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) PIDiff 61.40% -50.87 98.24% 86.95% -46.92 100% 7.69% -68.82 30.76% w/o finetuning 5.52% -55.88 100% 8.69% -44.08 100% 0.0 -72.28 100% Models TGFb (Seen) VirB8 (Seen) EGFR (Zero-shot) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) PIDiff 22.22% -49.29 22.22% 14.28% -48.31 100% 0.0 -48.35 100.0% w/o finetuning 0.0 -42.49 100% 14.28% -41.87 100% 0.0 -45.92 100% Models H3 (Zero-shot) IL7Ra (Zero-shot) Tie2 (Zero-shot) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) PIDiff 97.36% -47.08 31.57% 42.85% -50.42 100% 0.0 -42.39 100.00% w/o finetuning 44.73% -52.20 100% 14.27% -47.12 100% 0.0 -39.38 100% Models TrkA (Zero-shot) Average Novelty (↑ ) Diversity (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) SR (↑ ) Δ (↓ ) Consistency (↑ ) PIDiff 75.00% -46.04 75.00% 40.77% -49.85 75.78% 81.24% 29.08% w/o finetuning 0.0 -48.55 100% 8.72% -48.98 100% 83.32% 28.67% Table 21: Pretrained model performance on target-protein mini-binder complex design task. (↑ ): the higher the better. (↓ ): the lower the better.