ADFLIP: Inverse Protein Folding with All-Atom Flow

• ADFLIP is a generative model for inverse protein folding that designs sequences conditioned on complete all-atom structural contexts.
• It progressively integrates side-chain predictions and ensembles multiple conformational states to enhance contact specificity and design accuracy.
• Benchmark results show state-of-the-art performance in perplexity and recovery across complexes with small molecules, nucleotides, and metal ions.

Searching arXiv for the cited ADFLIP paper and directly related methods mentioned in the provided data. Search query: arXiv id (Yi et al., 4 Jul 2025) ADFLIP, short for All-atom Discrete FLow matching Inverse Protein folding, is a generative model for inverse protein folding that designs amino-acid sequences conditioned on all-atom structural contexts, including complexes containing small-molecule ligands, nucleotides, or metal ions, and can operate over multiple structural states such as NMR ensembles (Yi et al., 4 Jul 2025). It frames sequence design as a discrete flow-matching problem over amino-acid tokens, progressively incorporates predicted side-chain structure during denoising, supports training-free classifier guidance for sequence-level objectives, and reports state-of-the-art performance on single-structure and multi-structure inverse folding tasks (Yi et al., 4 Jul 2025).

1. Conceptual scope and problem setting

Inverse protein folding seeks a sequence of amino acids that adopts a target protein structure. In the formulation used by ADFLIP, the relevant target is not restricted to a protein backbone alone, but may include an all-atom environment containing non-protein components and, in the dynamic setting, a set of conformational states rather than a single static structure (Yi et al., 4 Jul 2025).

The model is motivated by two limitations identified for prior inverse folding methods. First, many such methods struggle on complexes that contain non-protein components. Second, they perform poorly when complexes adopt multiple structural states. ADFLIP addresses both by conditioning sequence generation on all-atom structural context and by averaging information across ensembles of structures during sampling (Yi et al., 4 Jul 2025).

This design scope places ADFLIP at the intersection of inverse folding, all-atom structural modeling, and conditional generative modeling. The paper situates this direction against the backdrop of recent progress in biomolecular structure modeling, noting that the breakthrough of AlphaFold3 in modeling complex biomolecular interactions creates new opportunities for protein design (Yi et al., 4 Jul 2025). A plausible implication is that inverse folding systems can increasingly be evaluated not only on isolated proteins but also on chemically heterogeneous complexes and conformationally distributed targets.

2. Discrete flow-matching formulation

ADFLIP casts sequence generation as a continuous-time, discrete Markov flow from a fully masked sequence to the target amino-acid sequence. Let

$s_t \in \{1,\ldots,20\}\cup\{m\}^L$

denote the sequence at time $t \in [0,1]$, where $m$ is a learned mask token and $L$ is sequence length (Yi et al., 4 Jul 2025).

The forward conditional law linearly interpolates between an all-mask state at $t=0$ and the true sequence $s_1$ at $t=1$:

$$p_{t|1}(s_t=i \mid s_1)= \begin{cases} t, & \text{if } i=s_1 \ 1-t, & \text{if } i=m \ 0, & \text{otherwise.} \end{cases}$$

Equivalently,

$$p_{t|1}(s_t)=\mathrm{Cat}\bigl(t\cdot \delta_{s_1,i} + (1-t)\cdot \delta_{m,i}\bigr).$$

The marginal at intermediate times is

$$p_t(s_t)=E_{s_1\sim p_{\mathrm{data}}}[p_{t|1}(s_t|s_1)].$$

To simulate transitions, the model introduces a rate matrix $t \in [0,1]$0 for $t \in [0,1]$1 such that, for infinitesimal $t \in [0,1]$2,

$t \in [0,1]$3

In practice, ADFLIP uses an Euler discretization with step $t \in [0,1]$4:

$t \in [0,1]$5

Learning proceeds by denoising. The reverse rates satisfy

$t \in [0,1]$6

with oracle conditional rate

$t \in [0,1]$7

Accordingly, the central learning problem is to approximate the posterior $t \in [0,1]$8 using a neural denoiser $t \in [0,1]$9, written as

$m$0

where $m$1 encodes side chains incorporated so far. Training samples $m$2, $m$3, and $m$4, removes side chains at masked positions, and minimizes the cross-entropy

$m$5

This construction makes ADFLIP a discrete generative flow over amino-acid tokens rather than a direct autoregressive or one-shot conditional predictor. The significance of that choice is functional: sequence generation is staged through a denoising trajectory in which structural context can be updated as more residues become fixed.

3. Progressive side-chain conditioning and all-atom context

A defining feature of ADFLIP is its progressive side-chain conditioning. The rationale stated in the paper is that side chains mediate most ligand, metal-ion and nucleotide contacts. Instead of conditioning solely on backbone geometry, the model interleaves sequence denoising with side-chain packing, so that newly predicted residue identities can contribute explicit atomic context to subsequent denoising steps (Yi et al., 4 Jul 2025).

Sampling begins from

$m$6

At each step, for each structure $m$7 in the input set, the denoiser computes

$m$8

These are averaged into an ensembled sequence distribution,

$m$9

A sample $L$0 is then drawn; for each conformation, a side-chain packer $L$1 predicts side chains

$L$2

The reverse step is applied, and $L$3 becomes the union of $L$4 over $L$5, with atoms removed at still-masked positions.

The operationally crucial rule is that once a position is sampled and is no longer masked, its side-chain atoms are permanently added to $L$6 for downstream denoising, whereas masked positions never carry side chains. This creates a progressive accumulation of atomistic context over the denoising trajectory (Yi et al., 4 Jul 2025).

In methodological terms, ADFLIP therefore differs from backbone-only inverse folding schemes by explicitly coupling sequence uncertainty to a partially realized side-chain environment. This suggests that the model is designed to improve sensitivity to chemically specific contacts at interfaces involving ligands, ions, and nucleotides.

4. Ensemble conditioning and training-free guidance

ADFLIP natively supports dynamic complexes by conditioning on multiple structural states. Given structures $L$7, the model feeds each conformation to the denoiser and averages the resulting conditional sequence distributions:

$L$8

In experiments on NMR ensembles with average $L$9, using all conformations simultaneously reduced perplexity and increased recovery by up to $t=0$0 relative to single-structure designs (Yi et al., 4 Jul 2025).

The same sampling framework also supports training-free classifier guidance. To steer generation toward a property $t=0$1 computed by a pretrained regressor $t=0$2, ADFLIP uses

$t=0$3

The method does not retrain $t=0$4 on partial sequences. Instead, during sampling it approximates the score $t=0$5 by the pseudo-gradient of $t=0$6 and reweights $t=0$7 accordingly (Yi et al., 4 Jul 2025).

Algorithmically, guidance proceeds by first computing the ensembled $t=0$8, then evaluating

$t=0$9

computing a guidance factor

$s_1$0

in logit space, reweighting the sequence distribution, and continuing with side-chain update and reverse discretization. The paper characterizes this as a plug-and-play scheme that can use arbitrary pretrained models, including AlphaFold confidence and DSMBind affinity, without retraining (Yi et al., 4 Jul 2025).

Two aspects are notable. First, ensemble conditioning and guidance are both integrated into the same denoising trajectory rather than treated as post hoc reranking. Second, the reported guidance results expose an explicit trade-off: property optimization can improve the targeted objective while reducing foldability relative to unguided sampling.

5. Architecture, dataset, and implementation

The training data comprise structures from the PDB satisfying the filters post-December 16 2022, resolution $s_1$1 Å, and $s_1$2 residues, followed by clustering at 30% identity by MMseqs2 (Yi et al., 4 Jul 2025). The resulting split contains 27 818 clusters in training and a held-out test set of 317 small-molecule complexes, 74 nucleotide complexes, and 83 metal-ion complexes.

The denoiser is a multi-scale GNN with atom and residue nodes. Its atom encoder uses Fourier embeddings of residue/chain indices, element/type one-hots, diffusion time, and local Invariant Point Attention with frame averaging. Its residue encoder uses $s_1$3-nearest neighbour geometric features (distances, angles) to both backbone residues and all non-protein atoms. The trunk alternates Local Atom Attention, Atom→Residue aggregation, message-passing GNN, and Residue→Atom scattering, with an optional non-protein context block and diffusion-time modulation. The decoder is a three-layer Transformer over residue nodes, with GeLU activations and a final linear layer to 21 logits (Yi et al., 4 Jul 2025).

For side-chain prediction, ADFLIP uses the PIPPack network $s_1$4, identified in the paper as PIPPack (Randolph & Kuhlman 2024), to predict $s_1$5 from $s_1$6 (Yi et al., 4 Jul 2025). Optimization uses the cross-entropy objective defined above, averaged over $s_1$7, sequences, and structures. The paper explicitly notes that it does not specify batch size, learning rate, optimizer, or regularization.

The implementation is publicly available, with code and pretrained weights released at the project repository. The repository-level interface supports design from a single structure or an ensemble, accepts non-protein inputs such as ligands, and exposes guidance settings such as DSMBind and a target gain parameter (Yi et al., 4 Jul 2025). This indicates a deployment model in which the research contribution is packaged not only as a benchmarked method but also as a reusable sampling system for new targets.

6. Benchmarks, performance, and interpretive context

ADFLIP was benchmarked against PiFold, ProteinMPNN, and LigandMPNN on held-out complexes. The primary metrics were perplexity, defined as $s_1$8 over interface residues, and sequence recovery rate, defined as the fraction of native amino acids recovered at masked positions. Foldability was assessed by refolding with Chai-1 and computing RMSD, TM-score, and pLDDT (Yi et al., 4 Jul 2025).

On small molecules, ADFLIP achieved perplexity 3.57 and recovery 62.2%, compared with LigandMPNN 3.84 and 59.2%, PiFold 4.03 and 59.2%, and ProteinMPNN 4.46 and 54.5%. On nucleotides, it achieved perplexity 4.86 and recovery 50.2%, versus LigandMPNN 4.97 and 46.1%. On metal ions, it achieved perplexity 2.61 and recovery 75.7%, versus LigandMPNN 2.73 and 69.3% (Yi et al., 4 Jul 2025). These results are presented as state-of-the-art performance on the tested single-structure tasks.

Foldability results follow the same pattern. For small molecules, ADFLIP reached RMSD 1.15 Å, TM 0.96, pLDDT 90.6, and 100% foldability, compared with LigandMPNN 1.21 Å, TM 0.95, 94.6, and 98.8%. For nucleotides and metals, the paper reports similar gains, giving as one example nucleotide RMSD 5.55 Å vs 5.99 Å (Yi et al., 4 Jul 2025).

The multi-structure setting is central to the method’s intended use. On NMR ensembles, using all conformations rather than a single snapshot improved recovery by +8.6% for small molecules, +5.8% for nucleotides, and +2.6% for metals, while reducing perplexity accordingly; ensemble foldability RMSD improved from 9.10 Å to 7.21 Å (Yi et al., 4 Jul 2025). These results support the claim that ADFLIP is not merely tolerant of conformational heterogeneity but is specifically designed to exploit it.

Classifier guidance introduces a more nuanced picture. With DSMBind and a target +10% binding gain, the unguided setting yielded 41.9% of designs exceeding wild-type affinity with 100% foldable, whereas the guided setting yielded 58.1% exceeding wild-type affinity with 91.4% foldable (Yi et al., 4 Jul 2025). A common misconception would be to treat guidance as universally improving all downstream properties simultaneously. The reported data instead indicate a targeted optimization mechanism that can improve the chosen property while reducing another criterion, here foldability.

Taken together, the empirical profile of ADFLIP is that of an inverse folding model specialized for all-atom, chemically heterogeneous, and conformationally distributed design problems. Its main technical identity derives from the combination of discrete flow matching, progressive side-chain conditioning, ensemble averaging across structural states, and training-free guidance, all within a single generative sampling framework (Yi et al., 4 Jul 2025).