Shrinking Proteins with Diffusion
Authors: Ethan Baron
Alan Nawzad Amin
Ruben Weitzman
Simon d'Oelsnitz
Debora Susan Marks
Andrew Gordon Wilson
Venue: ICLR 2026 Poster (2026)
Keywords: Proteins
Generative model
diffusion
discrete diffusion
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
TL;DR: We propose a discrete diffusion model that can learn to shrink proteins for bioengineering and medicinal applications.

Abstract: Many proteins useful in modern medicine or bioengineering are challenging to make in the lab, fuse with other proteins in cells, or deliver to tissues in the body because their sequences are too long.
Shortening these sequences typically involves costly, time-consuming experimental campaigns.
Ideally, we could instead use modern models of massive databases of sequences from nature to learn how to propose shrunken proteins that resemble sequences found in nature.
Unfortunately, these models struggle to efficiently search the combinatorial space of all deletions, and are not trained with inductive biases to learn how to delete.
To address this gap, we propose SCISOR, a novel discrete diffusion model that deletes letters from sequences to generate protein samples that resemble those found in nature.
To do so, SCISOR trains a de-noiser to reverse a forward noising process that adds random insertions to natural sequences.
As a generative model, SCISOR fits evolutionary sequence data competitively with previous large models.
In evaluation, SCISOR achieves state-of-the-art predictions of the functional effects of deletions on ProteinGym.
Finally, we use the SCISOR de-noiser to shrink long protein sequences, and show that its suggested deletions result in significantly more realistic proteins and more often preserve functional motifs than previous models of evolutionary sequences.

Published as a conference paper at ICLR 2026
SHRINKING PROTEINS WITH DIFFUSION
Ethan Baron New York University
Alan N. Amin New York University
Ruben Weitzman
Harvard University
Simon d' d'Oelsnitz Harvard University
Debora S. Marks Harvard University
Andrew G. Wilson New York University
ABSTRACT
Many proteins useful in modern medicine or bioengincering are challenging to make in the lab, fuse with other proteins in cells, deliver to tissues in the body because their sequences are too long. Shortening these sequences typically in- volves costly, time-consuming experimental campaigns. Ideally, we could instead use modern models of massive databases of sequences from nature to learn how propose shrunken proteins that resemble sequences found in nature. Unfortu- nately, these models struggle to efficiently search the combinatorial space of all deletions, and are not trained with inductive biases learn how delete. To ad- dress this gap, we propose SCISOR, novel discrete diffusion model that deletes letters from sequences to generate protein samples that resemble those found nature. To do so, SCISOR trains a de-noiser to reverse forward noising process that adds random insertions to natural sequences. fits evolutionary sequence data competitively with previous large models. In eval- uation, SCISOR achieves state-of-the-ar predictions of the functional effects deletions ProteinGym. Finally, we use the SCISOR de-noises to shrink long protein sequences, and show that its suggested deletions result in significantly more realistic proteins and more often preserve functional motifs than previous models of evolutionary sequences.
generative model, SCISOR
INTRODUCTION
As protein design becomes easier, more protein constructs are built for bioengineering, more pro- tein medicines are being packaged for delivery to particular tissues, and, of course, more protein is being synthesized in the lab. Unfortunately, many important proteins are challenging to make, engineer, and deliver, due to their long sequences. Methods to build shorter versions of these pro- teins are expensive and often only narrowly applicable. Typically, experimentalists look for shorter homologues, which may not exist, and put them through costly optimization campaigns (Huang ct al. 2022). Or, for proteins which function by well-characterized, simple biophysical interactions, experimentalists shrink sequences by running extensive physical simulations (Zhao al. 2023).
Ideally we could instead learn how to shrink proteins using models trained on databases of protein sequences nature these models learn the constraints evolution has put on sequences across life and could shrink proteins to avoid breaking their function. Unfortunately, these large models (Notin) al. 2022; Nijkamp et al. 2022) struggle effectively search through the massive space of all possible shrunken versions of protein. They may also lack the inductive bias to predict the effect of deletions, having not been explicitly trained to do so. In principle, the first issue could be solved by diffusion models of protein sequences, like EvoDiff, which are effectively trained to plan series of many mutations and end with sequences that resemble those found in nature (Alamdari et al., 2023 Luo et al., 2022). However, current diffusion frameworks can only train models that perform substitution mutations they cannot suggest deletions.
We propose new diffusion model of evolutionary sequences that learns to generate by shorten quences - Sequence Contraction with A'Sertion-Only noising pRocess (SCISOR). SCISOR adds noise to natural sequences by inserting random letters until they effectively become long random quences; then train a de-noiser to reverse this process by planning deletions that result in sequences that resemble those found in nature (Fig. Tap. Our contributions

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Random insertions (nolsing)
De-noise shrink
0.5
Xg
X MKVWFDIGPE
OEDINOMPNE
MICVANFOFDIGPE
JON
Deletion diffusion (SCISOR de-noising)
(a)
(b)
Figure I: SCISOR is a diffusion model trained to make deletions that arrive at a natural pro- tein sequence. We can use it to shrink proteins while maintaining their function. (a) We add random insertions to protein sequences from nature and train SCISOR to reverse these insertions. (b) Applying SCISOR diffusion to natural proteins, we get smaller proteins that are predicted to pre- serve parts of the tertiary structures of the original sequence. We show SCISOR samples of Q8NFU3 0, 5, 10, 20, and 50% deletion with structures predicted by OmegaFold (Wu et al. 2022).
We introduce SCISOR, a new discrete diffusion framework that trains de-noiser to generate sequences by learning to delete.
We solve practical limitations of previous discrete diffusion models, enabling us to scale SCISOR up large-scale evolutionary sequence data.
We show that among large-scale diffusion models, SCISOR achieves competitive model fit for protein sequences.
We show that the inductive biases of SCISOR allows to make state-of-the-art predic- tions of the effects of deletions on protein functions in the lab in ProteinCym.
Finally, we show that SCISOR shortens proteins while better maintaining their struc- ture and functional motifs than methods using previous models of protein sequences.
2 BACKGROUND
Say we have a protein sequence X made up of letters x()) (L)) belonging to the alphabet of 20 amino acids B. Our goal (())) ... with j1 < j2 < .......MMM that is still functional. Most random sets of deletions degrade the function of the protein, so we need to predict which deletions are unlikely to break the protein. Unfortunately there is very little data of sequence, shrunk-sequence pairs (X, X) learn from; we must instead learn to predict functional shrunk proteins using other available data.
remove M letters from X make X
Models of evolutionary sequences One way we can learn how to shrink proteins is by learning from modern huge datasets of natural proteins. Indeed we can attempt learn what a natural protein looks like in these databases; then we can pick a shrunken protein X so that it looks natural and is therefore likely to be functional" In practice, we can train huge generative models to generate natural proteins and use their likelihoods
measure of naturalness (Riesselman al., 2018 Rives et al. 2021 Notin et al. 2022; Nijkamp et al. 2022, Lin et al. (202)). Indeed, these likelihoods have will harm the function of a
been shown to be accurate predictors of whether single-letter-delee protein (Notin et al. 2022).
Unfortunately, the models that are typically used to fit this data, such as BERT-style (Rives et al. 2021 2 et al. 2202)) and autoregressive models (Notin et al. 2022; Nijkamp et al. (022), struggle to search the combinatorial space of all (M) possible sets of deletions to find ideal X. Ideally, we would have a model that can plan a number of deletions that arrive at a functional protein sequence. We also speculate that model that learns directly how to delete would make more accurate predictions and designs.
Discrete diffusion To effectively search through large mutational space, we could model the data with discrete diffusion models. These models generate samples by starting with a random sequence and applying mutations arrive a realistic sequence. In particular, sequence is sampled from simple distribution X, ((x)) and then it is transformed from time / = to 0 using a de-noiser
Note this does not guarantee goal that X have the same function X. But if two functional proteins have similar sequences then they often have related function (Mistry al. 2013). See also Sec. 9
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4o (X())) X1) so that Xg looks like sequence from the data generating distribution CCambelll cet al. 2022).
Diffusion models can therefore be used to search for sets of many mutations to a sequence, X, that result in a realistic looking sequence. To do so, one sets X, X for some s and then de-noises using the diffusion model by sampling a path q( giving realistic Xo near X.. Indeed,
this procedure has been used to suggest mutations to optimize sequences (Luo et al. 2022 Gruver al. 2023).
To train a de-noiser yo, we first define a forward process ((())===)) which takes samples from our target distribution Xo p(Xo), and applies random noise to them from time = 0 to / = 1, arriving at distribution that is easy to approximate p(X1). Then we train the de-noiser to generate paths that match the paths of the forward process by optimizing an evidence lower bound (ELBO) as
40 (o((X)) p p((xi))
log (Xo) 2 (p(( log
Typically, however, the forward noising process is chosen to be random substitutions. Accordingly, the de-noiser go only applies substitutions rather than deletions. To search over the space of dele- tions, we therefore need a new diffusion framework.
3 RELATED WORK
Diffusion models with insertions and deletions In chemistry and language modeling, there have been diffusion models that have attempted to allow for insertions and deletions. [Campbell et al. (2023) propose TDDM, jump diffusion model handle varying dimensionality, and Patel et al. 2025 train TDDM model on language. Their forward noising process involves randomly delet- ing elements, such that the stationary distribution is an empty sequence. This allows them to train model which can learn to expand sequences. As well, Johnson et al. (2021) formulate discrete-tie time noising process for scall-scale language modeling that includes insertions, deletions, and substitu- tions. Unfortunately their loss computation scales with the number of discrete time-steps and it is unclear how to extend their framework to continuous-tin rior (Campbell et al. 2022). Contemporary with this work, like Johnson et al. (202T). Havasi et al. (2025) use auxiliary tokens to describe a flow-matchin now-matching method for training a model to perform insertions and deletions in language.
diffusion, which is known to be supe-
Compared to these models, we train a diffusion model with inductive biases for the shrinking task. We also build models with competitive likelihoods to other generative models; in particular, like the models above (except Johnson et al. (2021) our model has a closed-form ELBO, which allows principled model comparisons. We solve various mathematical and practical problems that ultimately allow us to do so:
We prove that formal stationary distribution is not necessary to define diffusion model (Thm. D. This allows us to train diffusion model that only learns to shrink.
We extend the derivation in Amin et al.) (2025) to derive a "schedule conditioned" loss. This is more stable than classical discrete diffusion, and also allows us to condition on the number of deletions M (Thm. 4.2
We Rao-Black nooBBlackwellize our gradient estimator by integrating over all insertion paths. We do so in practice by noting a connection with sequence alignments (Prop. (P3)..4.3).
We solve number of engineering challenges to 1) pick an optimal rate function, 2) learn on very long sequences, and 3) leverage pretrained weights from ESM (Sec. 4.3)
Leveraging evolutionary data shrink proteins Recently, Raygun (Devkota al. 2024) also suggested using model trained on sequences from nature to shrink proteins. Raygun trains stochastic autoencoder to embed and generate sequences any length on the UniRef dataset which they apply variety of downstream tasks, including shrinking long proteins by decoding their embeddings at a shorter length. However, Raygun cannot enforce similarity between the shrunken sequence and original sequence. Furthermore, like previous generative models of protein sequences, Raygun was not specifically trained to shrink. Below we show that our model, SCISOR, suggests shrunken proteins that more often preserve structure and other indicators of function than Raygun.
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4 A DIFFUSION MODEL THAT LEARNS TO DELETE: SCISOR
To search the space of deletions and train a model with the right inductive biases, in Sec. 4.1 we build process which noises sequences by adding random insertions. Then in Sec. 4.2 we show how to train a de-noiser that reverses this process (Fig. Ta Finally, in Sec. 4.3 we discuss the practical choices we made efficiently train SCISOR. Sec. we describe how to use the de-noiser to generate sequences, shrink proteins, and plan deletions in practice.
4.1 FORWARD NOISING WITH THE PURE BIRTH PROCESS
We propose insertion-only forward noising process for discrete diffusion known as the pure birth process [endall 1948) with rate function Bt)) and insertion distribution т. Let Xo be a sequence X ................................ X There are L possible locations can insert letters. In the pure birth process, at instant t, each these locations gains an insertion with rate (t). The letter that is inserted drawn from some distribution Y Cat( After Y inserted at some position, the process continues and there are now L - 2 positions in which there could be insertions with rate B(t) (Fig. Ia). To train diffusion model reverse this process, we need approximate p( Xi (o))
easily sample p( Xo) and (2) easily
Sampling X, Rather than simulate the pure birth process up until time i, we show in App. G.1 that X₂ can be sampled directly from Xo as in Alg. | Note that 0 < att) S 1 controls how many insertions are added: by the property of negative binomial distributions, the expected length of X is M, + L a())
L+1 which grows as att) + 0.
Algorithm Sample X,
Require: Initial sequence X = x x(4,, time t
1: Compute the probability no insertions at a site a(t) + exp (- B(s)
2: Sample total number of insertions up time t, M, VegativeBinomial(1 at))
3: Sample the number of insertions in each position by uniformly distributing M, into L + bins:
(fo..... (1)) UnfformMultiomiaa((M
4: for j 0 to L do
5: Sample insertion Y, of length e,, with each character independently from Cat(T)
6: Add insertions into X to construct X, + (,, (,X x())),
7: return X,
Approximating (X)) As t grows, X₁ becomes longer. To build a diffusion model however, the distribution Xx) typically must converge distribution so that it can approximated by a distribution that can easily be sampled from, ((),). Our critical insight is that p(X, while not converging, can still be very well approximated by long random sequences as gets large.
Theorem 4.1. (Proof App. G.2 Say Xg sequence with length L. Call q( L) a distribution over sequences of length L which simply samples each letter independently from Cat(T). Then, as the number of insertions increases, Mi + oc, X, becomes easier to approximate with q:
(L(p(X, Xo, Mi)llg(X1 + Mi)) +
(2)
4.2 LEARNING TO REVERSE THIS INSERTION-ONLY NOISING PROCESS
Given forward process of insertions, we now wish to learn a de-noiser yo that generates sequences that resemble those found nature by deleting letters from long random sequences. We now (1) describe reverse process qo (X.))) (2) write the ELBO in Eqn. ] for model, and (3)
describe how the de-noiser qe is being trained toward a target that deletes letters that are unlikely to align with the starting sequence Xg-
The reverse process For a forward path (X)) from a sequence Xl of length L, define ti...., tv, to be the times of each insertion. We can then sample forward paths by first decid- ing how many insertions will occur until time 1 and when these insertions will occur, and then choosing what these insertions are:
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Mr
(((x))==o) p((t.)) M1, L)
((xts (e M=1
II
We follow the discrete diffusion framework in Amin et al. (2025) defining the reverse process to match the noise schedule of the forward process. To generate a sequence of length L, we first decide the number of insertions and their times from the same distribution as p, and then denoise each insertior
M1
go((X, (i) = p((1)))(((
() M1) II M=1
go (X
(eees M).
Now we must only train our de-noiser qe (X ( M) to take in a sequence Xtxr and the number of insertions that sequence has M, and predict the sequence before the last insertion Xta--1 That is, qo( , .M) can be thought of as a distribution over the letters X₁-
modify the caleulation of the ELBO from Eqn. [ as in Amin et al. (025). We will then use this ELBO as our objective for training the de-noiser.
The loss To train the de-noiser,
Theorem 4.2. (Proof in App. G.3) Define Mt the number of mutations up time and prev((,)) is the last sequence that gained an insertion to become X₁- Then the negative log likelihood of sequence of length L, log qo L), is smaller than
M,, (p(p No. (X))) Mi))
M,)(() + M,, a(t) (T(((prev(Xx)) Xo, Xx,
X2, M.)
The first term is the quantity in Eqn. 2 how well we can approximate p( (X1); it is small as long Mj is typically large, i.e. a<1) is small, and can be calculated as in App- B The second term is the quantity we use to train the de-noiser. qe takes in X, and the number of insertions in X₁ and must predict which letter of X, was last inserted prev(X,). To train the model, we must calculate p(prev(X,, No. X1, M,).
X
X,
Target distribution Eqn. trains qo to match p(prev(X.)) Xx, Xx, Mr). the true distribution over which letter of X, was last inserted in the forward pro- cess.
LGL
LLGALGL
--
-L GL
L--- GL
Conditioned on X X,, Mr. we could find prev (X,) by simulating a pure birth process path from Xo to X, and seeing what insertion occurred last. However there are multiple paths that could lead from Xo to Xx; to calculate p(prev(X, (X,) Xo. Xe, Mc), we must marginalize over all of these paths.
Alignments:
-LG- L
-LG
L-G---I
pddeletion Xx X, M)
# gaps:
The next proposition shows that we can integrate over all of these paths by first enumerating every way to align Xo to X, and noting that letters that align with X, less often are more likely have been prev(X,) (Fig. 2
target distribution of what letter to delete, (Xpr X,, Mr), we align our starting sequence Xo to our noised sequence X,. The reverse process should favor deleting letters that are gaps in more of the alignments.
Figure 2: To calculate
Proposition 4.3. (Proof in App. G.4 Call ali(X, Y) the number of ways align a sequence X sequence Y. Call b the letter that was deleted from X₁ to prev (re).
(X.) X,, M,) = ali(Xo, prev(X.))
Mr -aaaal(,, X,)
Naively computing this quantity would require running expensive alignment for every deletion. In practice, we use dynamic programming to computes all ali(Xo, prev(X.)) in parallel (App. H).
4.3 IMPLEMENTING SCISOR AT UNIREF SCALE
Our ultimate goal is to train large SCISOR models on huge protein data - in particular, the UniRef database (Suzek al. 2007). We train the SCISOR de-noiser with mini-batch gradient descent
Note our process is conditioned generating sequence of particular length T..
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t=1
t=0.5
t=0.25
t=0
M=10 M=50
M=150
Figure 3: The SCISOR de-noiser plans deletions to arrive at sequences that resemble those in nature, and therefore avoids deleting important structural motifs in natural sequences. (a) SCISOR unconditionally samples proteins by starting with large random sequence X₃ and itera- tively deleting according to ge (prev(X) (X, M) to arrive at a protein that resembles those nature. We predict the structure of each sequence with OmegaFold (Wu et al. 2022). (b) We ask SCISOR to plan the first of M mutations for R4SNK4 and color residue on a structure from Aleku et al.) 2016 by the deletion probability qe (x (-((=)) X, M). As increases, SCISOR favors deletions (red) in more regions while minimizing deletions in the catalytic structural motif near the bottom (white).
the second term of Eqn. with i.i.d. samples of t ~ Uniform (0, 1), Xo. M,, X, We now discuss how we choose the rate tunction ((t).. the distribution of insertion letters æ, the architecture for go. and methods to handle the large variation in sequence lengths of X₂ which we must pass to qo-
Hyperparameters Our choice of hyperparameters follows that of standard diffusion methods. As in Austin et al. (2021); Amin et al. (2025), the rate function ((() was chosen so that the mutual information between X, and Xo decreases roughly linearly on the interval / E [0. 1]. We then modulated 3 that (1) was large enough that the first term of Eqn. 3 is small, while samples in
the second term did not get to many very long X,. Details are in App. B The categorical distribution
was chosen to match the prevalence of amino acids in our training set.
Architecture We chose our architecture of the de-noiser 4o(-|X .)) to leverage the pre-trained weights of BERT-style protein language model, while modifying the architecture also condition on M. The ESM2 architectures (Lin et al., 2023) are trained on a masked language modeling task, taking in sequences and outputting logits at every site. We finetuned these models for qo by replacing their last layer with linear and softmax layer. To condition on M, we add FiLM layers (Perez et al, 2017] between attention blocks, such that coordinate of the activations in layer l, az is modified with affine linear transformation (1 (M))) x a + (M)) where Ag and Bg are shallow fully-connected networks initialized to zero.
Engineering for long sequences Since X; sequences can have wildly different lengths, training naively could result in passing batches with very high proportion of padding and passing very long sequences into the model. To avoid the first problem, we sort the X, sequences within a given batch by length, and pass them into the model in smaller sub-batches with accumulated gradients; this allowed us to reduce the proportion of compute spent on padding while maintaining an unbiased estimate of the loss. Next, handle
with extremely long X,, if [X.] 2048, randomly
selected window x X tu::+22018 uniformly at random to pass to the model. We then re-normalize the model predictions by 2048/|Xxr and use uniform predictions outside the window such that the deletion probabilities sum to 1. This choice keeps our ELBO valid lower bound on the likelihood.
Further details for how this impacts the ELBO and sampling are in App. B
USING SCISOR TO GENERATE AND SHRINK PROTEIN SEQUENCES
The SCISOR de-noiser qo is trained as a generative model of natural sequences. In this section, we describe how to unconditionally generate natural sequences. Then describe the statistical basis by which we may use the de-noiser for downstream tasks: predicting the effect of deletions on a protein's function, and, shrink long sequences produce shorter natural sequences.

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Algorithm 2 Unconditional sequence generation with corrector steps
Require: Desired sequence length L, corrector steps K
1: Sample M ~ NegativeBinomial(1 + 1, a(1))
2: Sample X length I. M where each X Cat(x) independently
3: while [X] L do
4: for k= to do
5: Remove one letter from X according to qo (prev(X)) |X, X)
6: Insert a random letter from the distribution и into random position in
7: Remove one letter from X according to qo (prev(X)) |X, M)
8: M +- M-1
9:
return X
High-quality unconditional generation As described in Sec. 4.2 to sample sequence of length L from SCISOR, one samples long random sequence from I E I X, [. + M1) and then iteratively deletes according to the de-noiser (Fig. 33). Campbell et al. 2023) suggests continuous-time discrete diffusion models can get higher quality samples, sacrificing some compute, by applying corrector steps which noise and de-noise repeatedly. For SCISOR, this takes the form of adding and removing insertions as Alg. 2 This allows SCISOR to more thoroughly search the space of deletions, potentially escaping local minima. In cases where many passes through the model is too expensive, we can make multiple deletions per de-noiser prediction, as discussed in App.
Mutation effect prediction Say have sequence X and we wish predict the effect of the deletion of every position to understand the importance of each residue. TTypically, we would take model trained on protein sequences, po and then evaluate the "natural-ness" of the sequence with each deletion (x(((=)) where X X!-O) is the deletion of letter i (Riesselman al. 20188. Unfor- tunately estimating the likelihood is challenging for diffusion models as one needs to estimate the
expectation in Eqn. [
SCISOR instead simply predicts qo (x(( X, MM 1) for every possible deletion X Then the de-noiser suggests that a residue is unlikely to deleted, that suggests that X without that residue does not look like sample from (Xo), i.e. a natural sequence, and thus that deletion may harm function. For multi-letter deletions, we integrate over all deletion paths (see App. B
Protein shrinking We consider the problem of shrinking sequence X by M deletions to new sequence X while preserving its function. One useful bias for this search may be using evolutionary information to look for X which are substrings of X which also look "natural". In practice, we can look for subsequences X which are higher likelihood under model trained on natural sequences. To do this, we can sample from (Xoo X X, M) which samples substrings in proportion to their "naturalness" (X, X). Indeed in App. D we show with three examples that deletions suggested by SCISOR correlate strongly with deletions seen in nature.
Note that SCISOR is not simply sampling deletions by how natural prev(X) looks. Rather it also uses knowledge of M to plan for future mutations. Different values of M allow the model to change which deletions it will allow each step (Fig [bb..
(bi..Bb). Given enough data and compute, SCISOR should learn the correct distribution go (X, = X X, M... In principle however, there is distribution shift between sampling go (Xn, X X, M) when is realistic protein and our learning process when X is sequence with noisy insertions; this may impact the statistical efficiency of the learning process. In practice, App. D and our results in the following sections show that the SCISOR de- noiser learns meaningful evolutionary signals. We also confirm this using toy example in App.
SCISOR IS A COMPETITIVE GENERATIVE MODEL FOR PROTEINS
We now compare how well SCISOR fits the distribution of natural sequences compared to estab- lished sequence modeling methods; see SCISOR fits sequence data well, competitively with state-of-the-an diffusion and autoregressive models. All details are in App.
In Fig. compare the quality of SCISOR's 's fit to the data against state-of of-the-atte-rrt protein diffu- sion models, EvoDiff (Alamdari et al. 2023) and DPLM (Wang et al., (024). and we include two autoregressive (AR) models from Alamdari al. (2023) references. All models are trained

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Figure 4: SCISOR fits the distribution of sequences in nature competitively with established sequence modeling approaches. (a) SCISOR is competitive with other diffusion models (grey) in perplexity. "S, M. L." refer to model size. (b, c) Samples from SCISOR (K = 5) are predicted to be competitive quality to those from diffusion models and competitive with AR models as measured by (b) matching the distribution of natural sequences as measured by the Fréchet protein distance (FPD) and (c) foldability (higher pLDDT from OmegaFold (Wu al. 2022)). We took EvoDiff and AR perplexities from Alamdari et al. (2023).
the same release of UniRef50 (uuzek al. 2007 small models have 35-38M parameters, DPLM M has 150M parameters, and large models have 640-650M parameters. We evaluate each model's perplexity on set, and the quality of their samples, as measured by how well they match the distribution of natural sequences (FPD), and foldability (pLDDT).
Despite its difference from established modeling methods, SCISOR competitive with other diffu- sion models in perplexities. As well, SCISOR often generates higher-qualine samples than previous diffusion models, even competitive with the reference. As mentioned in Sec. this is likely because SCISOR is continuous-time model while the other diffusion models are discrete-time. In App. [55] we ablate several components of our framework, particularly highlighting the importance of our Rao Bao-Blackwellized training objective.
STATE-OF-THE-AA
FUNCTIONAL EFFECT PREDICTIONS FOR DELETIONS
We evaluate SCISOR's 's ability to predict the effect deletion mutations on the function of proteins as measured in the lab. To do so, we use 7000 measurements of deletion effects from 62 assays baselines, we compare against existing mutation effect prediction models, including state-of-the-art autoregressive models ProGen2 (Nijkamp et al.) 2022) and Tranception (Notin et al. 2002). Since models trained on UniRef90 tend to better predict the effects of mutations (Rives et al. [2021) all models in this section are trained UniRef90.
collected in ProteinGym (Notin et al., 2023).
In Fig. 5 we report the Spearman correlations of the measurements of each assay against the pre- dicted effects from each model, taking the best performance within each model family (full table in F.I...I. SCISOR outperforms all baselines on both the single-deletion and multi-deletion bench- marks, even outperforming PoET (Truong & Bepler 2023), large model that has access extra information about protein families.
Single deletions
Multiple deletions
0.57
Spearman (T)
0.55
0.51
0.52
0.49
0.45
0.46
0.45
0.47
0.47
Tranception
HMM
Progen2
POET
SCISOR
Progen2
Tranception
HMM
POET SCISOR
Figure 5: SCISOR makes state-of-the-art predictions for the effect of deletions on protein function measured in the lab. We calculate the average Spearman correlation between predicted deletion effects and measurements across all assays in ProteinGym, presenting the results from the geghest-performing variant of each model architecture. Models that use multiple sequence alignment information are striped.
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Figure 6: SCISOR shrinks proteins while preserving their key properties. We take 200 UniProt
sequences with binding or active site annotations and shrink them by various amounts. We measure
(a) PLDDT structural confidence scores from Omegafold, predicted structural similarity between the original and shrunk proteins with (b) TM and (c) RMSD, and (d) conservation of annotated functional sites, measured by the enrichment ratio of annotated sites relative to random expectation. Horizontal dashed lines indicate reference values for 0% shrinking.
PRESERVING KEY IN-SILICO INDICATORS OF FUNCTION WHEN SHRINKING
We now evaluate the ability of the SCISOR de-noiser go to propose promising shrunk samples of long proteins from nature, Specifically, we take 200 sequences from UniProt that have binding or active site annotations and shrink them various amounts.
Since the diffusion models in Sec. 6 cannot suggest deletions, we compare as baselines to shrink- ing with ProGen2 and Raygun. Raygun requires model evaluation to make M deletions, while SCISOR requires M. For ProGen2, ideally we would sample substrings of X with length L M proportional to ProGen2's s likelihood; however, that would require (M) model evaluations, which is prohibitively expensive. We instead consider strong but tractable baseline: we predict the effect of all L single deletions independently (in L model evaluations) and then sample sets of deletions with probabilities based on these effects. Further details are App. Cand App.
In Fig. 6 we see SCISOR consistently suggests shrunken proteins that are more likely to be fold- able and preserve key indicators of function (predicted structural topology, presence of active or binding sites) than Raygun and ProGen2 baselines. Although ProGen2 achieves higher functional site preservation when shrinking by 50%, the lower PLDDT scores suggest that its samples at this level of shrinkage not likely to be functional. We stratify these results by Omegafold pLDDT, ESM2 saeudo-likelihood and cellular localization in App. [24]and and App.F.. In App. [F2, we show that SCISOR also achieves best performance for greedy sampling of shrunk sequences, reflecting situations in which a practitioner is not interested in generating diverse samples. Lastly, in App. [F] we perform an in-depth case study of shrinking the GTP sensor RalA, showing that shrinking with SCISOR best preserves the predicted structure of the binding site with GTP.
CONCLUSION
By proposing new family of generative models that learn build natural sequences by deleting. SCISOR, we have built models that can effectively shrink proteins. Future work may seek to address some of the conceptual limitations of the SCISOR process.
Realistic insertion process One way to mitigate the distribution shift mentioned in Sec. is to make samples from p(X,) look more like natural sequences with a more elaborate forward pro- cess. The challenge is finding process that provably achieves an easy-to -appro-appro p(X,) as in 4. and and deriving a closed-form integral over all paths as Sec. 4.2, Future work may leverage our theoretical and practical advances to derive the losses and train such models at large scale.
Guiding based on function In this work, we aimed to shrink proteins into sequences that may still appear in nature and are thus likely to be functional. While two functional proteins with similar sequences are likely to have the same function, this is not guaranteed, especially in those protein families with diverse functions (Zhang et al. 2024). Future work may incorporate other information of function into the SCISOR shrinking process. For example, one could guide the SCISOR diffusion process using classifier trained to detect functional proteins of interest (Nisonoff et al. 2024).
Including compensatory mutations Currently, SCISOR only shrinks proteins via deletions. is possible however that there are substitutions insertions that could be added protein to make

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it more tolerant to more deletions. To allow SCISOR introduce these mutations which planning series of deletions, we could add substitutions and deletions to the forward process, thereby training the de-noiser to also include substitutions and insertions in its planning.
ACKNOWLEDGMENTS
We thank Alex Ali and Andres Potapezynski for helpful feedback. This work was supported in part by NSF CAREER IIS-2145492, NSF CDS&E- MSS 2134216, NSF HDR-21 18310, BigHat Biosciences, and Capital One.
REFERENCES
Josh Abramson, Jonas Adler, Jack Dunger, Richard Evans, Tim Green, Alexander Pritzel, Olaf Ronneberger, Lindsay Willmore, Andrew J. Ballard, Joshua Bambrick, Sebastian W. Boden- stein, David A. Evans, Chia-Chun Hung, Michael O' O'Neill, David Reiman, Kathryn Tunyasuvu- nakool, Zachary Wu, Akvilè Zemgulyté, Eirini Arvaniti, Charles Beattie, Ottavia Bertolli, Alex Bridgland, Alexey Cherepanov, Miles Congreve, Alexander I. Cowen-Rivers, Andrew Cowie, Michael Figurnov, Fabian B. Fuchs, Hannah Gladman, Rishub Jain, Yousuf A. Khan, Caro- line M. R. Low, Kuba Perlin, Anna Potapenko, Pascal Savy, Sukhdeep Singh, Adrian Stecula, Ashok Thillaisundaram, Catherine Tong, Sergei Yakneen, Ellen D. Zhong, Michal Zielinski, Augustin Židek, Victor Bapst, Pushmeet Kohli, Max Jaderberg, Demis Hassabis, and John M. Jumper. Accurate structure prediction of biomolecular interactions with alphafold 3. Na- ture. 630(8016):493-500, 2024. ISSN 1476-4687. doi: 10.10388/41188-024--77777 10300.1088800
URL
https://aoi.
024 07487-w
Sarah Alamdari, Nitya Thakkar, Rianne den Berg, Alex Xijie Lu, Nicolo Fusi, Ava Pardis Amini, and Kevin K Yang. Protein generation with evolutionary diffusion: Sequence is all you need. bioRxiv, September 2023.
Godwin A Aleku, Henry Man, Scott P France, Friedemann Leipold, Shahed Hussain, Laura Toca- Gonzalez, Rebecca Marchington, Sam Hart, Johan P Turkenburg, Gideon Grogan, and Nicholas Turner Stereoselectivity and structural characterization of an imine reductase (IRED) from Amy- colatopsis orientalis. ACS Catal., 6(6):3880-3889, June 2016.
Alan Nawzad Amin, Nate Gruver, and Andrew Gordon Wilson. Why masking diffusion works: Condition on the jump schedule for improved discrete diffusion. In NeurIPS 2025, December 2025.
Jacob Austin, Daniel D Johnson, Jonathan Ho, Daniel Tarlow, and Rianne Van Den Berg. Structured denoising diffusion models in discrete state-spaces. Adv. Neural Inf. Process. Syst., 34:17981- 17993, 2021.
Andrew Campbell, Joe Benton, Valentin Bortoli, Thomas Rainforth, George Deligiannidis, and Arnaud Doucet. A continuous time framework for discrete denoising models. Advances in Neural Information Processing Systems, 35:28266 -22299, 2022.
Andrew Campbell, William Harvey, Christian Dietrich Weilbach, Valentin De Bortoli, Tom Rain- forth, and Arnaud Doucet. Trans-dimensional generative modeling via jump diffusion models. In Thirty-sevnnth Conference on Neural Information Processing Systems, November 2023.
Kapil Devkota, Daichi Shonai, Joey Mao, Young Su Ko, Wei Wang, Scott Soderling, and Rohit Singh. Miniaturizing, modifying. and magnifying nature's 's proteins with Raygun. bioRxiv, August 2024.
Robert D Finn, Jody Clements, and Sean R Eddy. HMMER web server: interactive sequence simi- larity searching. Nucleic Acids Res., 39(Web Server issue):W29-37) July 2011.
Cade Gordon, Amy X Lu, and Pieter Abbeel. Protein language model fitness is a matter prefer- ence. Bioinformatics, (biorxiv:2024. 10.03...........4...5... October 2024.
10

---

Published as a conference paper at ICLR 2026
Nate Gruver, Samuel Don Stanton, Nathan C Frey, Tim G Rudner, Isidro Hotzel, Julien Lafrance- Vanasse, Arvind Rajpal, Kyunghyun Cho. and Andrew Gordon Wilson. Protein design with guided discrete diffusion. In Thirty-sevntth Conference on Neural Information Processing Sys- tems, November 2023.
Marton Havasi, Brian Karrer, Itai Gat, and Ricky T. Q. Chen. Edit flows: Flow matching with edit operations, 2025. URL httph:tttpaaattttaee httpv//....g/aa///5..... 09011
Tony P Huang, Zachary J Heins, Shannon M Miller, Brandon G Wong, Pallavi A Balivada, Tina Wang, Ahmad Khalil, and David Liu. High-throughput continuous evolution of compact Cas9 variants targeting single-aclentide--yrrmiii PAMs. Nature Biotechnology, 41(1)) 107, September 2022.
Daniel D Johnson, Jacob Austin, Rianne van den Berg, and Daniel Tarlow. Beyond in-place corrup- tion: Insertion and deletion in denoising probabilistic models. In ICML Workshop on Invertible Neural Networks, Normalizing Flows, and Explicit Likelihood Models, 2021.
David G Kendall. On the generalized "birth-and-death" process. Ann. Math. Stat., 19(1):1-15,
March 1948.
Zeming Lin, Halil Akin, Roshan Rao. Brian Hie, Zhongkai Zhu, Wenting Lu, Nikita Smetanin, Robert Verkuil, Ori Kabeli, Yaniv Shmucli, Allan Dos Santos Costa, Maryam Fazel ZarandZa Tom Sereu, Salvatore Candido, and Alexander Rives. Fxolutionnar--calee prediction of atomic- level protein structure with a language model. Science, (1996667):1123-111 1130, March 2023. ISSN 0036-8075, doi: 10. .255 Epub 2023 Mar 16.
Shitong Luo, Yufeng Su, Xingang Peng, Sheng Wang. Jian Peng, and Jianzhu Ma. Antigen- -ppccifcc antibody design and optimization with diffusion-baat generative models for protein structures. In Advances in Neural Information Processing Systems 35. Cold Spring Harbor Laboratory, July 2022.
Claudio Mirabello and Björn Wallner. DockQ v2: improved automatic quality measure for protein multimers, nucleic acids, and small molecules. Bioinformatics, 40(10):btac886, 09 2024. ISSN 1367-4811. doi: 10. 00.009//iimfommaic//hee336 URL
bioinformat
Jaina Mistry, Robert Finn, Sean Eddy, Alex Bateman, and Marco Punta. Challenges in homol- ogy search: HMMER3 and convergent evolution of coiled-coil regions. Nucleic Acids Res., 41 (12)=e121, July 2013.
Erik Nijkamp, Jeffrey Ruffolo, Eli N Weinstein, Nikhil Naik, and Ali Madani. ProGen2: Exploring the boundaries of protein language models. arXiv [cs.LG], June 2022.
Hunter Nisonoff, Junhao Xiong, Stephan Allenspach, and Jennifer Listgarten. Unlocking guidance for discrete state-space diffusion and flow models. arXiv [cs.LG], June 2024.
Pascal Notin, Mafalda Dias, Jonathan Frazer, Javier Baarchena-Hurtadee Aidan Gomez, Debora Marks, and Yarin Gal. Tranception: Protein fitness prediction with autoregressive transformers and inference-time retrieval. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepes- vari, Gang Niu, and Sivan Sabato (eds.), Proceedings of the 39th International Conference Ma- chine Learning, volume 162 of Proceedings of Machine Learning Research, pp. 16990-17017. PMLR, 2022.
Pascal Notin, Aaron Kollasch, Daniel Ritter, Lood van Niekerk, Steffanie Paul, Han Spinner, Nathan Rollins, Ada Shaw, Rose Orenbuch, Ruben Weitzman, Jonathan Frazer, Mafalda Dias, Dinko Franceschi, Yarin Gal, and Debora Marks. ProteinGymm Large-scale benchmarks for protein fitness prediction and design. Advances in Neural Information Processing Systems, 36:64331- 64379, December 2023.
Dhruvesh Patel, Aishwarya Sahoo, Avinash Amballa, Tahira Naseem, Tim G Rudner, and Andrew McCallum. Insertion language models: Sequence generation with arbitrary position insertions. arXiv [cs.CL.), May 2025.
11

---

Published as a conference paper at ICLR 2026
Fred Zhangzhi Peng, Pranam Chatterjee, and contributors. FAESM: An efficient pytorch implemen- tation evolutionary scale 2024.
hect:s//gg.haa...co///eeeggaagap faeam
Ethan Perez, Florian Strub, Harm de Vries, Vincent Dumoulin, and Aaron Courville. FiLM: Visual reasoning with general conditioning layer. arXiv [cs. CVJ, September 2017.
Adam J Riesselman, John Ingraham, and Debora S Marks. Deep generative models of genetic variation capture the effeets of mutations. Nat. Methods, 15(10):816-8) 822, October 2018.
Alexander Rives, Joshua Meier, Tom Sercu, Siddharth Goyal, Zeming Lin, Jason Liu, Demi Guo, Myle Ott, C Lawrence Zitnick, Jerry Ma, and Rob Fergus. Biological structure and function emerge from scaling unsupervised learning to 250 million protein sequences. Proceedings of the National Academy of Sciences, 118(5)):2016239) 18, 2021.
Baris E. Suzek, Hongzhan Huang, Peter McGarvey, Raja Mazumder, and Cathy H. Wu. UniRef: comprehensive and non-redundant UniProt reference clusters. Bioinformatics, 23(10):1282- 1288, 03 2007. ISSN 1367-4803. doi: 10. 00.0093hionnfommacicsttM009 URL https:
Timothy Fei Truong, Jr and Tristan Bepler. PoET: A generative model of protein families as sequences-of-sequenees. In Thirty-seventh Conference Neural Information Processing Sys- tems, November 2023.
Xinyou Wang, Zaixiang Zheng, Fei Ye, Dongyu Xue, Shujian Huang, and Quanquan Gu. Diffusion language models are versatile protein learners. ICML, abs/2402. 18567, February 2024.
Ruidong Wu, Fan Ding, Rui Wang, Rui Shen, Xiwen Zhang, Shitong Luo, Chenpeng Su, Zuo- fan Wu, Qi Xie, Bonnie Berger, Jianzhu Ma, and Jian Peng. High-resolution de novo structure prediction from primary sequence. bioRxiv, pp. 2022.07.21 25.09999, July 2022.
Jinrui Xu and Yang Zhang. How significant is protein structure similarity with tm-score = 0.5? Bioinformatics, 26(7):889-888 895, April 2010. ISSN 1367-4803 doi: 10. 1099///ooinfoormacic// http:://ww.....//.ooooooooo.../.
btq066. URL
Mingyang Zhang, Ting Chen, Xun Lu, Xiaobing Lan, Ziqiang Chen, and Shaoyong Lu. G protein- coupled receptors (GPCRs): Advances in structures, mechanisms and drug discovery. Signal Transduction and Turgeted Therupy, 9(1):1-43, April 2024.
Yang Zhang and Jeffrey Skolnick. Scoring function for automated assessment of protein structure template quality. Proteins, 57(4)7002-710 December 2004.
Feiyu Zhao, Tao Zhang, Xiaodi Sun, Xiyun Zhang, Letong Chen, Hejun Wang, Jinze Li, Peng Fan, Liangxue Lai, Tingting Sui, and Zhanjun Li. strategy for Casl3 miniaturization based on the structure and AlphaFold. Nat. Commun. 14(1):5545, September 2023.
Yixiu Zhao, Jiaxin Shi, Lester Mackey, and Scott Linderman. Informed correctors for discrete diffusion models. arXiv Lcs. July 2024.
A CODE RELEASE
We release our code at http:///hhub..cmm/arrrrrttt/ssss and model weights for SCISOR small (35M), medium (150M), and large (650M) trained on UniRer50 and UniRef90
B DETAILS ABOUT SCISOR
B. PRIOR MATCHING KL TERM
We rewrite the first term of Eqn. estimate it.
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Proposition B.1. (Proof in App.
G
(p(pp
Xo, M1) + M1)) is equal to
Mi
Ex, Mo,
log
+
log log (Xx')) - log ali(Xo, xi)
(4)
L
We can therefore estimate the first term of the loss in Eqn. by sampling Xo, M1, X₁ as calculating the quantity in the expectation of Equ.
B.2 EFFICIENT SAMPLING
Alg. 2 implements the Gillespie algorithm for stochastic process. Zhao et al. (2024) and AAmin
ct al. (2025) suggested k-Gillespie for diffusion models, taking steps at every step by sampling
without replacement. Indeed we can do the same for SCISOR, sampling many deletions at each step without replacement.
B.3 MULTI-DELETION PREDICTION
Say X is the sequence X with M deletions sites ( i.r). We wish calculate go go
X X, M). We can break this up into a sum over all deletions using the de-noiser
M
(x = X,
Σ m=
go (Xo = X (mm)), M - 1)gg - ((-im) M,
Continuing like this, we can write (X, = X M) as a sum over all permutations of the deletions.
Algorithm Predicting the functional effect of multiple deletions with SCISOR
Require: Initial sequence X, deletions (i1,-...im}
1: P t- all permutations of {i....., 3
2: SUM +
3: for fi,..., jMs P do
4: SUM SUM II 40 (x(( (X((-tt x(-timmdd))) M³)
5: return SUM qo (Xo X X, M)
B.4 RATE FUNCTION
For simplicity, we choose a functional form
7
3(t) = 1 - tmaxt
Consequently, have:
all)= exp
3(s) ds
=xx
tuax /o
ds
t
exp
In(1 tmaxt)
tmax
=(1
maxx))
t)7/tman
and (11 = (1 (max Mm Now we must choose 7 and fmax. We found empirically small models that 7 = 1.1 gave an ELBO (see Eq. 3 such that the expectation conditional on each t roughly even. We found empirically small models that tmax 0.9 gave the best best loss controlling for wall time, trading off allowing the model to attempt to fit larger sequences and spending compute those large sequences.
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B.5 WINDOWING
One challenge in efficiently training the SCISOR de-noiser that we must compute (o Mr), where X₁ can potentially be a very long sequence. To handle these long sequences, we introduce windowing strategy: if [Xx]] 2048, we randomly select window X (w::++2055) uni- formly at random to pass to the model. We then re-normalize the model predictions by Xal (the probability of deletion in the window is proportional to its size) and use uniform predictions outside the window such that the deletion probabilities sum to 1. Calling the predictions made by window w 9ø (prev(X,) X,, M,), we can define our model predictions as an average over all windows
qo (prev (X,) Xx, M,)
g (prev Xx, Mt).
ELBO We modify the second term of our loss Eqn. to obtain another lower bound to bring the expectation outside
KL(p(prev(X.)) Xo. Xt, M.) (p)revv)()))(( Xx, M,)
(Lp,e (X,) Xo, Xx, Mc)lla (prev(X,) | X,, M,)).
This gives us new ELBO we can estimate by stochastically sampling the window whenever we get a large sequence.
Sampling In Alg. need to sample from qo (X;.) Mr) for very long sequences. We
do so by sampling w and then sampling from qp (prev(X;) X1,
C EXPERIMENTAL DETAILS
C.I BASELINES
We used EvoDiff models and code from under the MIT license. We used DPLM models and code from https: com/ bytedance/ /aapnnc///lpmmmmm under the Apache-2.0 license. We used ProGen2 models and code from https://githut
under the BSD-3-clause license. We used Raygun models and code conm/eniiiaappp/pogggen comp wttp:///ww......ii...a.aaaaaaaaa
com/enii
under the CC BY-NC 4.0 license. We used ProteinGym models and code from https: com/ under the MIT license.
C.2 SCISOR ARCHITECTURE
We used the flash attention implementation ESM from Peng et al. (2024) under the MIT license. We used ESM2 weights (Lin al.) (203) also under the MIT hieese. We developed SCISOR using code from /ottps://qittie com/ foo/Aa anNawzadAmi iataaamii/scuuu under the MIT license.
C.3 TRAINING SCISOR
We apply our framework to train protein generative model on UniRef50 (Suzek et al.) (007). We filter this dataset to exclude proteins with non-standard amino acids, and crop long protein sequences down their first 1024 amino acids.
For the results in Section 6 we train SCISOR models on the March 2020 release of UniRef50, using the same train-test split as EvoDiff (Alamdari et al.) 2023) from ht zenodo. org/ records / 65 64 798] Our models were trained about one week each one NVIDIA A100 GPU with an effective batch size of 256 and learning rate of 0.0001.
For the results in Sections 7 and g train SCISOR models the latest release of UniRef90. Here, we use an effective batch size 512 and learning rate of 0.00005. The SCISOR S and M models trained for about trained for about four days on four NVIDIA H100 GPUs.
week each two NVIDIA A100 GPUs. The SCISOR L model was
For each effective batch, sampled all Xo. Mr, X,. We then sorted sequences by the length of X, before breaking them into batches to pass to the model in batch sizes of or 16; This makes sequences in each batch have similar length, minimizing padding.
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C.4 MODEL HIT EXPERIMENTS
C.4.1 PERPLEXITIES
4a on the test dataset by first sub-sampling the expectation of the ELBO from Prop- 4.2 we take TO samples of i, X2 for every sequence. We then by the total number of tokens in the test set and report the exponentiated negative result.
SCISOR We compute the perplexity in Fig.
EvoDiff and AR We take perplexity values from Table SI in Alamdari et al. 2023
DPLM DPLM trained discrete- timettte-tmmeeeeee masking diffusion model with 500 steps and linear rate schedule that is, the probability of each token in X, being masked is t/500. We therefore evaluated their perplexities such model in Austin al. (2021). This ELBO becomes
500
L
Ex X Σ
1(x
mask) log go (X, | X2).
C.4.2 SAMPLES
SCISOR
We sampled according to Alg.
EvoDiff and AR We sampled from EvoDiff and AR models www.etiionnneeeerttee..aaaaaaaa on and generate.autoreet from
ma main/evod: ff/generate.pp
DPLM Wang al. (2024) suggested novel sampling method for DPLM. However, we were terested in measuring the quality of DPLM samples as diffiusion model. We therefore took samples as such model as in Austin et al. (202T): : We start with X and for every 500, we unmask each position with probability I/ replacing the mask according to predicted probabilities
(X X+).
C.4.3 SAMPLE EVALUATION
For FPD we took 1000 protein lengths from UniRef50 and sampled sequences of each of those lengths from SCISOR, EvoDiff, and DPLM; or we sampled 1000 sequences from the AR models. For pLDDT, we sampled 100 sequences of length 100, 200, 400, and 800 from SCISOR, EvoDiff, and DPLM; for AR models where the sample length cannot controlled, we sampled sequences until we had sufficient number of samples with lengths within 10% of each desired length.
Fréchet protein distance (FPD) We calculated the FPD of 1000 generated sequences to 10000 samples from UniRef50 using ProfT5 embeddings in https: thub. com/ hww.eeffeeee//// PGP under the Apache-2.0 license. We then calculated the Fréchet inception distance between the em- beddings of the natural sequences and each set of sampled sequences
Unntural /sampell|
Enatural Example 2(Enatural ssappee)
where and E. are empirical means and covariances of the embeddings.
PLDDT We calculate pLDDT scores using OmegaFold (Wu al. 2022 described in
/ttps://qithub.. com He wtt.ioooooooeoeeeeeeeeeeeeee httpod/d/llb//oooooooooooooohhtt b RaEAAADn//EAEE.... mdl un- der the Apache-2.0 License. For computational efficiency, only cycle per sample. This results in lower overall PLDDT scores than the recommended default settings, which uses 10 cycles obtain more accurate predicted structures.
C.5 PROTEINGYM
C.5.1 MODEL. PREDICTIONS
SCISOR To evaluate SCISOR, X₂ to be the target sequence and M to be the number of deletions between the target and the mutant of interest. We then predict the effect of the deletion using Alg.
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ProGen and other models
We evaluated other models using scripts available ProteinGym.
C.5.2 MODEL EVALUATION
For Fig. adapt the ProteinGym benchmark from (Notin et al. 2023) by filtering their indels dataset to cases where the mutant is a strict subsequence of the target sequence. For the single deletions benchmark, while for the multiple deletions benchmark, we use mutants that are two or three deletions away from the target sequence.
mutants that only deletion away from the target sequence,
For single mutations, we gathered 61 assays in ProteinGym with 4544 mutations in total.
Three assays in ProteinGym measured double and triple mutations: A4_HUMAN_Seuma measured stability and had 42 double mutations and 40 triple mutations, MOUSE Macdonald.200 387 triple mutations, P53 HS3.AAMAN... Kotler-201 measured organismal fitness and had 172 double mutations and no triple mutations.
KCNJ2.MOUSE
measured expression and had 397 double mutations and
C.6 SHRINKING
For Fig. and 6d we sample 100 sequences with annotated active sites and 100 sequences with annotated binding sites from UniProt. We then shrink each sequence by d percent, where d e (1,3,5, 5, 10, 20, 30, 40, 50).
C.6.1 MODEL SAMPLES
SCISOR We shrunk sequences using Alg. 2
ProGen Ideally we could sample from (rroGen (X) over all shrunken versions of X, X, of desired length L- ... However, for even moderate values of M, this becomes computationally intractable. We therefore approximate this distribution by assuming each deletion has an independent effect:
log (rroGen (X) x log PrroGen (X) +
Σ
4
deletious 8
where A; is the effect of single mutation,
A log ProoGen (X
ProGen (X)
This approximation requires calculating L quantities A,
Sampling from this approximation is equivalent to sampling M deletions deletion i is sampled with probability proportional to cxp(A,). Greedy shrinking just involves picking the M mutations with the highest A:
Raygun we use the Raygun generate command to generate shrunken proteins of desired length, where length was calculated by first calculating rounded up number of deletions introduce, and conditioning Raygun to generate sequence of length L M. we used noise ratio of 0.5 with uniform sampling (noise sampled uniformly between and 0.5), in order to limit the number of substitutions introduced. We use filter ratio of 0.1 meaning we select the best candidate among ten generated sequences, and recycle sequences once.
C.6.2 MODEL EVALUATION
We evaluate the foldability the shrunk sequences using the average PLDDT per residue for the structure generated using OmegaFold (Wu et al. (2022 as described in https:://ittht
main/ README. må under the Apache-2.00 2.0 Li- cense, using cycle per sample. We caleulate enrichment the number of active binding sites in the original sequence that were preserved in the shrunk sequence we call a functional site "pre- served" if residues modified or deleted.
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D SCISOR DELETIONS MATCH THOSE IN NATURE
We collected sequences locally aligned three proteins using the phmmer web (Finn al. 2011) (open penalty=0.. 01, Extend=0 2, and all other settings default) and counted how frequently each position of each sequence landed in region that wasn't 't aligned ("Not aligned"") or aligned with a gap token ("Gap"). These are two distinct ways to measure deletions made by nature. Next, we shrunk each sequence using SCISOR various values of M, taking 512 samples for each M. We ran our analysis on catalyst BASNK4_9PSEL membrane transporter TPIS HUMAN, and transcription factor FOXAI HUMAN.
In Fig. 7 we plot, for each position of each protein, how frequently we observe deletions sug- gested by SCISOR versus as seen in nature. We see strong correlation between the samples from SCISOR and those from nature. Almost all comparisons model never achieves a Spearman correlation above 0.015, while we achieve a p-value of < 10-10 10 for each protein.
statistically significant random
Interestingly, for BUSNKK-_PPSEL we observe separate behavior at different M: we see qualitatively that M 50, SCISOR prefers making deletions in regions where gaps observed in nature, while at M 100 SCISOR prefers deleting large chunks of the protein, the region which was less frequently included in alignments.
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aligned
Gaps
SCISOR (M 50)
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1.0
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270
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(a) R4SNK4 9PSEU
(b)
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SCISOR (M = 60)
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(e) FOXAI HUMAN
(
Figure 7: SCISOR suggests deletions seen in nature. (a, c, e) We compare two ways to measure deletions in alignment versus deletions at two values of M from samples of SCISOR. (b, d, f) We quantitatively measure the Spearman correlations between the two types of deletions in our alignment deletions in SCISOR samples across M.
E CASE STUDY: SHRINKING RALA
To better understand SCISOR's ability to shrink natural proteins, we perform a detailed case study of the RalA protein, of length 206. We chose RalA since, GTP sensor, could easily tell which sequences were unlikely to be functional by predicting their bound structure to GTP. We evaluate the function of shrunk samples by predicting their binding to GTP in the structure _dl_00000110 00001uad and comparing to RalA. We use Alphafold (Abramson et al. 2024) to predict the structure of shrunken RalA, GTP and binding partner Sec5.
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Qualitative results We measure the TM score papolar measure of structural similarity ground truth (Zhang & Skolnick, 2004)) of wild type and shrunken RalA residues within 10 angstroms of the GTP molecule. Following Xu & Zhang 20100,, use TM=0.5 function and evaluate 5 designs for each method. The results are presented in T We see that proteins shrunk with SCISOR much more likely adopt the complex fold the wild type compared to designs from other methods.
liberal cutoff for non-
Deleted
Random
Raygun
ProGen2
SCISOR
I
5
5
5
5
3
4
5
5
5
5
5
5
3
5
10
1
1
5
20
0
1
0
5
Table Number designs not predicted non-functional (TM scores above 0.5) (out of 5)
Quantitative results Next we show similar results with various measurements of the quality of the interface between the designed RalA and GTP. In Table 2 perform structural alignment using the RalA structures and then calculate the RMSD for residues within 10 angstroms of the center of mass of the GTP. In Table and rotated GTP. Additionally, we report DockQ values (Mirabello & Wallner) 2024) in Table and the iM scores from Alphafold in Table In all these results, we we see that SCISOR consistently outperforms all baselines, suggesting that the candidate designs from SCISOR are most likely to preserve the function of the original RalA protein.
instead calculate the RMSD of the atoms of the translated
% Deleted
Random
ProGen2
Raygun
SCISOR
0.90 = 0.13
0.87 0.10
1.02 + 0.23
0.92 0.01
3
1.52 = 0.24
1.25 + 0.15
0.89 189=00 0.11
0.91 091:000
5
1.64 = 0.15
1.48 0.37
0.87 0.17
0.93 0.00
10
1.83 + 0.23
1.93 + 0.28
1.03 + 0.11
1.24 0.14
20
2.07 0.30
2.28 0.18
2.37 + 0.11
1.28 + 0.15
Table Interface RMSD of residues within 10 Å of GTP after structural alignment.
% Deleted
Random
ProGen2
Raygun
SCISOR
1.69 + 0.30
4.03 + 1.67
7.39 4.82
2.07 0.56
3
3,91 + 2.04
(04
3.47 + 0.53
2.37 + 0.36
6.19 + 3.20
3.53
15.24
3.50 0.72
10
10.92 + 5.29
11.47
12.19 4.13
3.95 + 1.24
20
17.83 5.55
10.06 1.52
15.24 1.89
10.32 + 2.81
Table 3: Ligand RMSD of GTP atoms after structural alignment.
% Deleted
Random
ProGen2
Raygun
SCISOR
1
0.86 + 0.04
0.71 + 0.17
0.38 + 0.15
0.87 0.01
3
0.50 0.20
0.51 0.18
0.62 0.15
0.85 1 0.02
5
0.46 + 0.18
0.18 + 0.11
0.23 + 0.13
0.88 + 0.01
10
0.36 0.15
0.18 0.15
0.13 0.10
0.50 + 0.18
20
0.13 + 0.11
0.11 + 0.07
0.03 - 0.02
0.30 + 0.16
Table 4: DockQ scores for RalA binding to Sec5 with standard error.
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Deleted
Random
ProGen2
Raygun
SCISOR
I
0.83 = 0.07
0.82 0.08
0.60 = 0.07
0.90 = 0.00
3
0.64 + 0.11
0.71 + 0.08
0.82 + 0.08
0.90 + 0.00
5
0.67 + 0.09
0.52 0.08
0.51 + 0.01
0.89 + 0.00
10
0.40 = 0.14
0.47 0.13
0.59 + 0.07
0.67 + 0.09
20
0.22 + 0.06
0.36 + 0.06
0.42 + 0.03
0.58 + 0.09
Table 5: ipTM scores from AlphaFold for RalA binding Sec5.
F SUPPLEMENTARY RESULTS
F.1 FULL PROTEINGYM RESULTS
We show the results for ProteinGym for all models and sizes, stratifying the single deletions into functional, taxonomic, and MSA depth categories.
Table 6: ProteinGym results single and multiple deletions.
Model
MSA
Single Deletions
Multiple Deletions
ProGen2 S
0.457
0.445
ProGen2
0.513
0.385
ProGen2 Base
0.497
0.408
ProGen2 L
0.491
0.375
ProGen2 XL
0.393
0.392
RITA S
0.409
0,274
RITA M
0.448
0.318
RITA L
0.465
0.323
RITA XL
0,440
0.161
Tranception S
0.439
0.475
Tranception
0.464
0.424
Tranception L
0.445
0,426
HMM
Yes
0.453
0.474
PoET (200M)
Yes
0.551
0.488
SCISOR S
0.332
0.268
SCISOR M
0.505
0.520
SCISOR L
0.573
0.492
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Table 7: ProteinGym results single deletions stratified by the measured function of each assay.
Model
MSA
Activity
Expression
Organismal Fitness
Stability
ProGen2
0.566
0.294
0.499
0.470
ProGen2 M
0.574
0.404
0.558
0.514
ProGen2 Base
0.592
0.380
0.496
0.520
ProGen2 L
0.550
0,344
0.560
0,508
ProGen2 XL
0.418
0.298
0.333
0,521
RITA S
0.507
0.320
0.452
0.356
RITA M
0.514
0.345
0.500
0.432
RITA
0.530
0,437
0.420
0.474
RITA XI.
0.532
0.385
0.360
0.481
Tranception
0.542
0,351
0.532
0.331
Tranception M
0,594
0,340
0,526
0.395
Tranception L
0.533
0,336
0.445
0,466
HMM
Yes
0.496
0.321
0.501
0.493
PoET (200M)
Yes
0.664
0.424
0.566
0.551
SCISOR
0.376
0,289
0.198
0.465
SCISOR M
0.514
0.362
0.576
0.571
SCISOR
0.604
0.415
0.668
0.606
Table 8: ProteinGym results on single deletions stratified by the MSA depth of proteins in each assay.
Model
MSA
Low
Medium
High
ProGen2 S
0.558
0.429
0.497
ProGen2 M
0.415
0.483
0.544
ProGen2 Base
0.438
0.460
0.568
ProGen2 L
0.513
0.473
0.532
ProGen2 XL
0.216
0.499
0.530
RITA
0.300
0.293
0,424
RITA M
0.278
0.376
0,492
RITA L
0.444
0.434
0.504
RITA XL
0.139
0.462
0.508
Tranception S
0.467
0.316
0.360
Tranception M
0.297
0.358
0.447
Tranception L
0.519
0.391
0.518
HMM
Yes 0.624
0.506
0.471
PoET (200M)
Yes
0.595
0.553
0.548
SCISOR
0.385
0.381
0.509
SCISOR M
0.641
0.547
0.575
SCISOR
0.621
0.628
0.584
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Table 9: ProteinGym results on single deletions stratified by the taxa the protein in each assay.
Model
MSA
Human
Eukaryote
Prokaryote
Virus
ProGen2 S
0.506
0.467
0.361
0.567
ProGen2 M
0.536
0.539
0.432
0.510
ProGen2 Base
0.568
0.541
0.396
0.471
ProGen2 L
0.536
0.513
0.442
0,492
ProGen2 XL
0.511
0.537
0.420
0.573
RITA S
0.398
0.353
0.272
0.448
RITA M
0.496
0.417
0.310
0,504
RITA L
0.522
0.473
0.327
0.568
RITA XI.
0.510
0.466
0.386
0.555
Tranception S
0,332
0.363
0.297
0.449
Tranception M
0,443
0,406
0.295
0,468
Tranception L
0.511
0.462
0.348
0.513
HMM
Yes
0.585
0.392
0.437
0.547
PoET (200M)
Yes
0.554
0.522
0.523
0.721
SCISOR
0.486
0.418
0.340
0.652
SCISOR M
0.571
0.539
0.525
0.735
SCISOR I.
0.590
0.568
0.621
0.767
F.2 DETERMINISTIC SHRINKING
In Section we report results for sampling shrunk sequences from SCISOR and baseline models. Those evaluations are most relevant to practical settings, where practitioners may wish to generate a diverse set of promising candidate designs be evaluated in the lab. Here, we instead consider deterministic shrinking. where the most likely deletions are performed. For Raygun, mimic this setting by using setting the noise parameter to O. In Fig. we see that SCISOR consistently achieves excellent performance in this setting well. Although ProGen2 achieve higher performance in some cases, this method is more computationally expensive than SCISOR. Moreover, our metrics may be rewarding the "myopic" nature of ProGen2 baseline, which likely favors deletions that preserve functional regions in the original protein that are not necessarily functional in the shrunken protein.
Random
ProGen2
Raygun
SCISOR
0.8
1.6
pLDDT
60
RMSD
1
Fnc Ennch
1.4
1.2
0.2
1.0
% Deleted
% Deleted
% Deleted
Deleted
(a)
(b)
(c)
(d)
Figure 8: Deterministically shrinking proteins with SCISOR yields high-quality shrunk sam-
ples. All details are as in Fig. 6 except that we take the most likely deletions predicted from each model. For Raygun, we noise 0.
F.3 COMPUTATIONALLY EXPENSIVE PROGEN2 BASELINE
In Section 8 we reported baseline for ProGen2 that required L. forward passes of the model, already exceeding the forward passes used by SCISOR. That baseline assumes that the effects of each deletion are independent, which may be unrealistic. In Fig. D we present results for more expensive ProGen2 baseline, requiring O(L .M) forward passes, where deletions are performed one at time, and the effects of subsequent deletions recalculated. We that switching this more expensive ProGen2 baseline does not improve performance, and SCISOR remains the best- performing method.
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Random
ProGen2 - oLL)
ProGen2 OILM)
SCISOR OIM)
0.8-
Fnc Enrich (T)
RMSD (4)
BLDDT
0.6
1.1
0.4
0.9
30
0.2-
0.7
1 10 20 30 % Deleted
50
3
5 10 20 30 40 50 Deleted
10 20 30 40 50 % Deleted
3
5 10 20 30 50
Deleted
(a)
(b)
(c)
(d)
Figure 9: SCISOR outperforms expensive ProGen2 baseline. All details are as Fig. except that we include more expensive ProGen2 baseline that requires O(L-M (LM forward passes compared to SCISOR's (M)
F.4 SHRINKING RESULTS STRATIFIED BY WILD TYPE PLDDT AND ESM2 PSEUDO-LIKELIHOOD
In Fig. 10 we show how SCISOR's shrunk designs compare to the baselines, stratified by the Omegafold PLDDT quartile of the wild type. SCISOR consistently produces high-quality designs across all settings, confirming its robustness.
Random
ProGen2
Raygun
SCISOR
TM
RMSD
Enrich
1.4
0.8
70
04
60
3.5
1.0
30
10
20
30
50
16
20
30
40
50
10
20 Deleted
30
40
50
36
20 Deleted
30
40
56
% Deleted
Del cted
80
1.4
70-
03
80
0.6
1.2
0.4
1.0
30
5
10
20
30
40
50
5
10
20
30
40
50
10
20
30
40
50
5
10
20 Deleted
30
40
50
% Deleted
etle
Deleted
80
1.4
70-
0.6
1.2
0.4
1.0
40
30
0.2
0.8
5
10
20
30
40
50
5
10
20
30
40
50
5
10
20
30
40
50
5
20
30
40
50
% Deleted
% Del eted
Deleted
%
Deleted
80
1.4-
70
0.6
1.2
0.4
40
30-
0.8
5
10
20
30
50
10
20
30
40
50
5
10
20 Deleted
30
50
5
10 20
30
50
%
Deleted
% Deleted
%
Deleted
Figure 10: SCISOR consistently predicts high-quality shrunk designs for wild type proteins with various PLDDT scores. All details are as in Fig. 6 and we facet results by quartile wild type PLDDT score, predicted by Omegafold.
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In Fig. show how SCISOR's shrunk designs compare the baselines, stratified by the ESM2 pseudo-likelhood quartile of the wild type, similar to the analysis in Gordon et al. (0024). The pseudo-likelhoodd is calculated by masking element, and then aggregating the scores across the full sequence. SCISOR consistently produces high-quality designs across all setrings, confirming its robustness.
index time, computing the likelihood of that
Random
ProGen2
Raygun
SCISOR
PLDDT
TM(
RMSD (4)
Fnc Enrich (T)
1.4
0.8
Q4
60-
0.6
50
1.0-
0.2
20
50
20
50
20
50
20 Deleted
30
50
Deleted
Del eted
Deleted
0.8
1.4-
Q3
60
0.6
50
1.0-
20
50
20 Deleted
50
5
20
50
20 Deleted
30
Deleted
Deleted
1.4-
0.81
70
Q2
60
0.6
1.0
30
10
20
30
50
10
20
30
40
50
5
10
20
30
40
50
10
20 Deleted
30
40
50
Deleted
Del
Deleted
1.4
70
01
60
0.8
1.0
30
10 20
10
50
16 20 Deleted
30 40
50
10 20
30
40 50
16 20 Deleted
10 40 56
1% Deleted
Deleted
Figure 11: SCISOR consistently predicts high-quality shrunk designs for wild type proteins with various PLDDT scores. All details are as in Fig. [ and we facet results by quartile of wild type pLDDT score, predicted by Omegafold.
F.5 ABLATIONS OF MODELLING CHOICES
We perform an ablation study training SCISOR S on Uniref50, ablating two aspects our model. In Fig. 12a
that structured forward process which weights amino acids by
their prevalence results in slight speedup of training. contrast, in Fig. 12b we see that the Pao-Blackwellizzttion described in Section 4.2 crucial in enabling the model learn efficiently.
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SCISOR
Uniform
No Rac Blackwellization
Trivial
3.0
Perplexity (J)
Perplexity (1)
2.9
2.8
2.7
2.7
25000
50000
75000
25000 50000 75000 Step
Step
(a)
(b)
Our structured forward process and Rao-Blackwellizatioon of the loss enable effi- cient training of SCISOR. We train SCISOR S on Uniref50 sequences, ablating components of our framework. While (a) switching from uniform distribution over amino acids to one that weights amino acids by their prevalence results small improvement, (b) the weolBlackwellized loss is crucial to efficient training of SCISOR. The random baseline is based on the entropy of the amino acid distribution in Uniref50. We plot an exponential moving average of the perplexity on a withheld validation set.
Figure 12:
F.6 FEATURES ENRICHED IN PROTEINS THAT ARE HARD TO SURIINK
We investigated the differences between proteins in the analysis in Fig, 6 hypothesizing that mem- brane proteins may be more challenging to shrink. In Fig. 13 we find no enrichment membrane proteins among the sequences whose structure dropped the most in quality after shrinking. This potentially because they often contain large regions outside of the membrane, or because intra- membrane regions are not particularly sensitive to deletions. A preliminary analysis did reveal slight enrichment of extra-cellular proteins however.
90
membrane
extracellular
20% deleted PLDDT
80
60
40
40
60
80
starting PLDDT
Figure 13: We do not have evidence membrane proteins harder to shrink. We plot the results of Fig. 6 for 200 proteins. We plot the PLDDT of the full-length protein against that shrunk 20% by SCISOR. We colour membrane and extra-cellular proteins.
G PROOFS
G.1 PROOF OF CORRECTNESS FOR ALGORITHM
The correctness of Alg. follows from Cor. G.2
Theorem G.I. Call
x,=
(2)... x( (
where x( (1)) x(2) x..)() are the letters of Xu and Yo, ..... YL are the insertions. Then Yil is Geom(a(t)) distribution, where alI) exp( (s)
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Proof. By the Kolmogorov forward equation,
d
P m)() - 3())p(()ii =n - --1)) (())++++)))) 1)p((11))()))) m/().
di
This can be written as
(clntt) P(s)do p(|xi = nltt) = nn Sa (()))d = -1)).
dt
For n = O, this is solved by p( = 0lt) att). By induction,
p( |i| = n/t) = a
as
na(t)-(n=)) ((t)p(()) = nn - 1 =nx(()) "/(()) a(t))==
(5)
(a(t) "(1 a(t))*)
Corollary G.2.
P( (EE)) = a(t) (tt) [X]
so P( (Yrl)) only depends on [Xol and M = E.IYi In particular we can sample M ~ NegativeBinommallco and then distribute uniformly into L 1 bins.
Proof. Each Yíss generated independently, so we just take the product of probabilities from Prop. G.I
G.2 PROOF OF THEOREM 4.1
Theorem G.3. (Proof of Thm. 4.1 Say Xo sequence with length L. Call g(- L) distribu- tion over sequences of length L which simply samples each letter independently from Cat(T) for distribution π such that T(() > for all letters b. Then, as the number of insertions increases,
M1 + 0c, X1 becomes easier to approximate with q:
KL(p(X, Xo, Mo),Ma)lll(X. L M1)) +
Proof. We suppress the subscript 1. Note by Lem. G.8
p(X XD, M) (X
ali( Ali(Xo, X)
L + M)
(L+M (xx
For a set of indices I = i < is < ... < iL, call X1 = 1(x, = x .(()))). Then
ali(Xo, X) = E, XI and EaxI= 11 a (x(")) Therefore we can write
p(X Xo, M)
X)
Ep log {X L +MM
Ep log
(L++M) I (x)
ali(Xo, X)
Ep log
Egali (X)
ali(Xo, X)
E.p
E,aai((X (Xo, X)
Ep lali(Xo, x) Egali X)1
(No; X)
Ep Jali( X) Epali(Xo, X)
Faaai((Xo. X)
Epali(Xo, X) EEgai((o, X)I
Exali(Xo, X)
Stdp (ali(Xo, X))
Epali(Xu, X)
Exali(Xo,
Exali(Xo, X)
We now show that these terms each go to 0, starting with the second term.
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The second term Say X is generated by picking indices Z 21 < then generating all other letters from πT Say we have indices I. Then
2L which are Xu and
Exxr S(1 p Z = 0)) + Esp lxll/n
(M+1-11)
+ EgxT
(M
M - L)
+ EgXt
M
00 (L' /M) + EgxI
-11 o(1))
Also
Epxi 2(1 p( 1In==1 0)) Ex -
x EqxT
(M
M
4
x Fxgx
M +
2 (1 (1-0 O (L3 (L2/ /M) EqxI
-(1 ((1)
Then
E,ali(Xo, X) (xa
(M+1) Epxt o(1)
The first term We first change the expectation in the standard deviation into an expectation over Say X is generated by picking indices Z = 21 < ... < 21. which are Xg and then generating all
other letters from Say we have indices J. Then
Epxix_ S(1 - p(1n Z, nz 0)) + E, 2 = 0]
<1 (M+L-2XL)
EaXIXs
(Mth)
=0(L² (M) + Eqxixx.
We also have from above that
Exx = (1+(()))))
Then
(MM)))
M I. I, o(1) Σ Covy(xi,X))
2
Yar,ali(Xo, = Σ Covp(xxxx))=
L
I.J
The first term is (1) against Exali(Xo, -M++H) (Ex1)², so we can just focus on the second term, Var,ali(Xo, X).
Note [J== = then xx) = Then
M + L.
M (M+
L
M (M+L)) )
using the same logic above. Therefore, Var,ali(Xo,, X) o (M)t)²) (EE,al((Xo,))? X)2). This completes the proof.
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G.3 PROOF OF THEOREM 4.2
Theorem G.A. (Proof Thm.. 4.2) Define Mr as the number of mutations up time and prev (X+) is the last sequence that gained an insertion to become Xt- Then the negative log likelihood of sequence of length L, llog qo (Xu)L), L), is smaller than
BM, (T,(p(X1 Xo, ( (1T.4 M1)) M,3(()
(T.(ppprev(Xt) Xo, Xt, Mi)ll((peexx))) Xx, Mc)) + M,, 1 ((t)
Proof.
The proof of Prop. 4.4 from Amin et al. (025) derives an ELBBO
(L((L(((, | Xo, Mi M1)llg(X1144 M)))
+ R,,, w/ M, 1, X (p)peee (x) Xo, X,, go)llo Xe, M.)
where
w (MM, t, X.) = lim E[#events in M, c-+
The following lemma shows this result.
Lemma G.5.
3(t)
wf (M,4,XX)) = M 1-a a(()
Proof. First we change out time variable to r =====- - at). Noting - log - = - c3(Tr) + O(e2), we have
(M,ttXoo) 3(t) lim #events in [T e, 7]|MM [M]/E c-0
(6)
where E is as if the rate 3 were constant. In SCUD, events occur uniformly in the time interval, so the RHS would M/T = M/(- log (t)). For SCISOR, events are more concentrated later in time since more insertions increases the rate of insertion.
E #events in [ T,M, M] -PM --c = M 1|M, M]
Pl = M - --------1
PIM,
PMM, M|
Note
P(M, M M, M =P[M; M M, = M -
=P(EXp(M (Xol) +c)+((())
(8)
=1 - -1 (MMMXXX0))) +0(2)
=e(M + (Xol) + +((e).
Finally,
P(M, M - 1]
NegBin([Xoo/ e T 1)
P(M, M]
NegBin( Xo) E M)
(m-1+1Xol)) (1 -
m-
(9)
( (1 --
M
(M (Xol) =-=
This gives us
w M,,, Xo) M 3(t)
1-a(t)
which is similar for small alpha to the SCUD weight of w(M, L, Xo) larger at larger values.
M but becomes
[(8)
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G.4 PROOF OF PROPOSITION 4.3
Proposition G.6. (Proof of Prop. 4.3) Call ali(X, Y) the number of ways align a sequence to a sequence Y. p(prev(X;)) X,, M,) = oo (0o.prev(X))
M, ali(Xo, Xx)
Proof. Say Y, is X, with a single deletion, the letter By Lem. G.8
P(4 Xo, X,, M.) p(Ge Xo, Mr - 1)
P(X; Y))
p(X, Xo. M,)
1 -1 ali(Xo: Yi)
TLb) M))
(b)
(L Mo)ali(Xo. Yr)
(xali(Xo; Xx)
ali(Xu, Yi).
M,ali(Xo, X,)
Note finally that we've ignored that there may be multiple deletions that take X, to Y, when cal-
culating p(X, Yt). We can safely do so as it does not affect the loss Eqn. 3 of any of our other algorithms.
G.5 DERIVATION OF PRIOR MATCHING KL TERM
Proposition G.7. (Proof of Prop.
B.l KT(p(X,
|
Xo, ()] M()) equal
Ex, MX
log
M1 + L
+
log log (x(')) - log oogali(Xo, X1)
L
1=1
Proof. From Lem. G.8
p(X1 M1) (Mi + L
ali(Xo, X1)
II
T(6).
L
Given that g(X, M1)
-bbex Tbb), this finishes the proof.
G.6 USEFUL LEMMA
Lemma G.8. Calling the letters in X, that are not in Xo X, \ Xo.
p(X,1 No, M.) = L Mi) (L++MM)) ali(Xo, X2)
-1
T(b)
beX,XXo
Proof. To generate X, from Xo, Mc. could (1) decide which positions é1, ....... d E 1, 1,..., L + Mj should come from Xy and then generate the rest of the letters according to æ. Then
1(Xo = x((1)) (1))
p(X, Xo. Mc) =
Σ
II beX,
T(6)
(L+M))))
indices iE....i
L Mi)
ali(No, X,)
II ((b).
bEX,XXo
29

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Published as a conference paper at ICLR 2026
H ALIGNMENTS ALGORITHM
Both KL terms in the ELBO make use of the primitive ali(X, Y). In particular, the denoising KL requires computing the number of alignments between Xg and each possible prev(X;); total of [Xel computations. Naively, computing the alignments between each pair of sequences takes (oo Xxl) time for a total of O[ |x,l). However, we devise an efficient dynamic programming algorithm to compute all of the alignment terms in parallel in O( |Xel) time, presented in Algorithm 4
Algorithm Compute ali(X; ( Xo) for all I in parallel
Require: Sequences X, with |.ool = L and X, with [xx]= = N
Set matchinglé, ( .] < I(x; ) for all i (1..... L). (1....,N)
2: Initialize prefix dp <- ([++1)
3: Set prefix_dpfi, 0] <- for all i E (1,...,N)
4: for /o 1 to L
matching!! - : 6: prefix.dp11: N + 1, < cumsum(prod, axis = 0)
5: prod 4 pwwppreeeixxxx <d[x /
7: Initialize suffix.dp + 1x++)x
8: f down to do
down
9: prod < suffix dp 1 N + 1,1+ + 1] x matching (7, : N] cumsum (pronu axis 0)
10: suffix_pp11 N,
11: alignments[]] + Σ pp I] suffix dpli + 1, + 1] for all
12: return alignments
30

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Published as a conference paper at ICLR 2026
I EXPERIMENT WITH TOY SYNTHETIC DATASET
There is a distribution shift between the sequences SCISOR sees during training composed of unnatural sequences with potentially many random insertions and the inputs wish to when shrinking natural proteins. To show that this distribution shift is not a fundamental issue for SCISOR, perform experiment with toy synthetic dataset designed capture this challenge.
Specifically, our toy synthetic data has an alphabet of A, B, C, but assumes that the only functional sequences those that alternate A and B, such as "ABABABABA". The length of functional quences is sampled uniformly at random between 1 and 20.
During training, due to the random insertions, SCISOR is exposed mostly sequences that not valid, such as "ACBBABCCBAB" Nevertheless, when we apply SCISOR to shrink a valid sequence, it should learn to only return valid subsequences. Indeed, Fig. [4 we see that this is the case: within half an hour of training. SCISOR samples >99% functional subsequences from functional sequences. All training details are the same as for our protein experiments, except use smaller batch size of 64.
Shrink valid sequences
Random
SCISOR
Learn to shrink invalid sequences
ABABABABABAAABABA
Random insertions
ABABAB
AABABABBABA
0.8
0.6
ABCABBAB
AABABABA
0.4
CABACABBAB
AABABB
CBAABACABBABE
ABAB
0.0
10000
CBAAECACCABBABSA
Step
(a) SCISOR trains on out-of-distribution data
(b) SCISOR learns to shrink valid sequences
Despite being trained on unnatural sequences, SCISOR able shrink natural sequences while preserving validity. (a) We train SCISOR S on toy synthetic dataset where natural sequences are alternating As and Bs, such that the random insertions noising process results in primarily invalid sequences. (b) We find that despite being trained to shrink invalid sequences, SCISOR quickly learns to shrink valid sequences as well in less than 30 minutes of training. Here, plot the percent of alternating sequences of length L 20 which SCISOR shrinks to another valid sequence after M 10 deletions.
Figure 14:
31


Reviews:
[{"review_id": "4HMl6dTHao", "reviewer": "Reviewer_Ryfk", "summary": "This paper introduces SCISOR, a new discrete diffusion framework designed to “shrink” protein sequences by learning to delete amino acids while maintaining functional integrity. The core idea is to train a denoiser to reverse a pure insertion-only forward process (a pure birth process), effectively teaching the model how to delete. SCISOR is trained on evolutionary sequence data, learning to remove randomly inserted amino acids to recover natural sequences. The trained denoiser is then applied to shorten real protein sequences.\n\nThe authors claim that SCISOR achieves state-of-the-art deletion-effect prediction on ProteinGym, and that its suggested deletions preserve functional motifs and structural integrity better than prior generative sequence models such as ProGen2 and Raygun.", "questions": "1. Could the authors justify—either theoretically or empirically—why reversing random insertions is a good proxy for learning function-preserving deletions?\n2. What would happen if the forward process included deletions (as in TDDM) instead of insertions? Would the model’s generative behavior improve or degrade?\n3. How sensitive are the shrinking results (Fig. 6) to the sampling strategy for ProGen2 and to the hyperparameters of the corrector steps?\n4. Could the authors provide TM, RMSD, and Fnc Enrich metrics for the stronger baseline discussed in Appendix F.3?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. **Motivation relevance**: The paper tackles a meaningful biotechnological problem—designing shorter, more manufacturable proteins.\n2. **Technical creativity**: The proposed insertion-only diffusion and the use of sequence alignment to marginalize over insertion paths is elegant and mathematically nontrivial.\n3. **Empirical performance**: SCISOR performs well on ProteinGym deletion benchmarks, outperforming established baselines in both single and multi-deletion effect prediction.", "weaknesses": "1. **Training–application mismatch**:The model is trained to reverse random insertions ($p(X_0|X_0+noise)$) but applied to delete residues from real sequences ($p(X_{shrunken}|X_0)$).This mismatch creates a serious distribution shift, acknowledged but not resolved. It remains unproven that a denoiser trained to remove random noise can effectively identify biologically nonessential regions for deletion.\n2. **Unfair or weak baselines**: The main “shrinking” baseline (ProGen2) assumes independent single deletions—a simplified and unrealistic setup. Although a more accurate sequential baseline ($O(L⋅M)$) is mentioned in Appendix F.3, it is not the focus of comparison, and key results (e.g., TM, RMSD, Fnc Enrich) for that stronger baseline are missing.\n3. **Computational cost**: Training SCISOR is extremely expensive. Computing $p(prev(X_t) | X_0, X_t, M_t)$ requires dynamic programming over all deletion alignments $(O(|X_0||X_t|)$, repeated for each batch. This forced the authors to apply window approximations, potentially biasing the training.\n4. **Functional preservation remains indirectly validated**: The assumption that “naturalness” (model likelihood) correlates with function retention is reasonable and common in protein LMs, but the current evidence is largely in silico. Including further structural or biochemical proxies — e.g., energy-based metrics, functional-domain conservation, or experimental validation — would significantly enhance the biological credibility of the work.", "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": "N23xSWASEx", "reviewer": "Reviewer_Xm99", "summary": "SCISOR is a discrete diffusion framework for protein miniaturization. The forward process inserts residues into natural sequences; the learned reverse process deletes them, enabling principled exploration of the deletion space. Trained on large protein corpora with an ESM-style backbone, SCISOR attains strong accuracy on deletion-effect prediction (ProteinGym) and, for design, shrinks diverse UniProt proteins while preserving in-silico foldability (pLDDT), structural similarity (TM/RMSD), and functional-site retention better than LM baselines at moderate shrinkage.", "questions": "- Generalization tests: How does performance vary across enzymes, membrane proteins, or multi-chain interfaces, where small deletions can disrupt dynamics or binding? Any oligomeric/complex benchmarks planned?\n\n- Experimental readouts: Can you report ΔTm, expression yields, solubility, etc. for a set of shrunk designs to calibrate pLDDT/TM against real biophysics?\n\n- Search strategy: For multi-deletion design, how sensitive are results to sampling vs. greedy selection? Any gains from guidance (classifier-free or property predictors) to target function preservation explicitly?\n\n- Boundaries of shrinkage: Where is the failure frontier (e.g., % deletion where foldability or motif retention collapses) across diverse families?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- Right inductive bias for deletions. By making the forward process insertions, the reverse process naturally learns deletions. That’s a clean, principled way to search the combinatorial deletion space.\n\n- Design-oriented evaluation. The UniProt shrinking study checks multiple in-silico proxies (pLDDT, TM/RMSD, motif enrichment) and shows consistent gains over ProGen2 and Raygun for realistic shrink amounts.\n\n- Scalable implementation details. Uses ESM2 + flash attention; training/data choices are clear enough to be reproducible.\n\n- Clarity about scope. The paper is explicit that SCISOR currently performs deletions only, which makes contributions and limitations crisp.", "weaknesses": "- Wet-lab validation is limited. The main evidence for design quality is in-silico (structure confidence/similarity, motif enrichment). Experimental assays beyond ProteinGym measurements would strengthen claims (e.g., stability, activity, expression yields).\n\n- Function vs. foldability tradeoffs. At very aggressive shrinkage (e.g., ~50%), some baselines can retain more annotated sites while losing foldability; SCISOR’s behavior under extreme compression could be characterized more deeply (kinetics, dynamics, allostery).\n\n- Backbone dependence. Performance and generalization lean on the ESM2 backbone and training corpus; robustness across families with sparse data or disordered regions isn’t fully explored.\n\n- Template-free but prior-bound. Although not template-conditioned, SCISOR is still guided by evolutionary priors; novel functions that deviate from natural sequence statistics may remain hard.", "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": "AacEiQXSZF", "reviewer": "Reviewer_RVrd", "summary": "The paper proposes SCISOR, a discrete diffusion model that learns to shorten protein sequences while preserving their structural and functional integrity. Instead of using additive noise like standard diffusion models, SCISOR defines insertions as the forward process and deletions as the reverse process, allowing it to model sequence shrinking directly.  Theoretically, the author prove that a stationary distribution is unnecessary for defining a valid diffusion process, derive a schedule-conditioned loss for stable training and introduce a Rao-Blackwellized gradient estimator by integrating over all insertion paths via sequence alignment. Empirically, SCISOR achieves competitive perplexity and structure-based scores compared to leading generative baselines, and demonstrates superior preservation of foldability and active sties when applied to protein shortening tasks. Overall, the work establishes a principled and scalable deletion-based diffusion framework for biological sequence generation", "questions": "Considering the weaknesses outlined above, I have a few questions and suggestions that could help clarify the empirical evidence and strengthen the paper’s claims if addressed in the rebuttal.\n\n1. Do you have any evidence that large-scale (20–50%) deletions predicted by SCISOR retain actual biochemical function?\n2. Have you checked whether OmegaFold results and model rankings remain consistent when using the optimal settings ( such as 10 cycles instead of 1)?\n3. How robust is SCISOR to the mismatch between insertion-noised training sequences and natural inference inputs?\n4. Can you provide validation on more proteins or families beyond the single R4SNK4 example?\n5. Since SCISOR optimizes for natural-looking sequences, how do you ensure that key functional domains are not deleted?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper is original in both formulation and problem scope. It extends discrete diffusion to irreversible deletion processes by defining a continuous-time insertion-only forward process and a deletion-based reverse process, effectively removing the symmetry assumption of prior discrete diffusion models. This enables a principled treatment of the protein shortening problem, a biologically relevant task that has not been previously modeled in this way. The theoretical development is coherent and well integrated, combining the continuous-time formulation, schedule-conditioned objective, and alignment-based gradient estimator into a unified framework. Empirically, the model achieves good results on both sequence and structure-based evaluations. The paper is clearly written, effectively linking theoretical innovation with practical biological relevance.", "weaknesses": "Despite the paper’s strong theoretical formulation, its empirical evidence for true functional preservation remains incomplete. The following issues address key gaps between the model’s assumptions, its training evaluation setup, and its stated goal of maintaining biological function after large-scale deletions.\n\n1. Validation Gap  \n**Limited experimental validation**: ProteinGym provides experimental measurements only for 1-3 deletions, but the main application involves 20-50% shrinking (50-100+ residues). While computational metrics show SCISOR outperforms baselines at large scales (Fig. 6), there's no experimental validation that these predicted improvements on large-scale deletions correlate with actual functional retention.  \n**Unvalidated surrogate metrics**: For large-scale shrinking, the paper relies entirely on predicted metrics without validating their correlation with actual function. Additionally, structure predictions use suboptimal parameters: OmegaFold with 1 cycle instead of recommended 10 cycles, acknowledged to produce \"lower overall pLDDT scores\" (App. C.4.3). No validation that method rankings remain consistent with proper parameters.\n\n2. Distribution shift underexplored  \n Training uses sequences with random insertions while inference uses natural proteins. Authors acknowledge this (Sec. 5) but provide only one validation example (R4SNK4, App. D) showing modest correlations (Fig. 7b, mostly <0.5). More examples across diverse protein families would strengthen the claim that the model learns meaningful evolutionary patterns despite this mismatch.\n\n3. Fundamental Gap  \n**\"Natural-looking\" Does Not Guarantee Functional Preservation**:   SCISOR optimizes for shrunk sequences that look \"natural\" (high q_θ(X̃)), but this does not guarantee they maintain the original protein's function. A shrunk sequence can achieve high naturalness by resembling a common domain found in nature, while completely losing other functional domains of the original protein. Example limitation: Consider a 500-residue transcription factor with a DNA-binding domain (100 aa) and activation domain (400 aa). SCISOR might produce a 200-residue shrunk version containing only the DNA-binding domain. This would score high on naturalness and structural metrics (pLDDT, TM), but would completely lose transcriptional activation function.  \n**Metrics don't validate functional retention** (1) pLDDT measures foldability, not specific function. (2) TM score measures structural similarity, but high TM doesn't guarantee functional preservation, e.g., deleting an allosteric regulatory domain can maintain high TM while abolishing regulation. (3) \"Functional enrichment\" only checks if annotated sites exist, not whether they remain functional in the altered structural context.  \n**Acknowledged but understated**: The paper admits \"similar sequences are likely to have the same function, but this is not guaranteed\" (Sec. 9), yet frames SCISOR as a protein engineering tool throughout. This gap between \"generating natural-looking subsequences\" and \"preserving specific function\" is fundamental to the method's practical utility but receives insufficient discussion.", "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": "T7WF0f630B", "reviewer": "Reviewer_xiN6", "summary": "This paper introduces SCISOR, a generative diffusion model designed for protein shrinking, learning to remove amino acids from natural proteins while maintaining functional and structural integrity. The proposed model reformulates sequence diffusion where the forward process inserts tokens, and the reverse process learns to delete them. The authors derive an exact training objective with two KL terms and compute analytical expressions for event intensity.The paper also demonstrates competitive performance on protein sequence modeling (UniRef50/90), strong correlation with natural deletion patterns, and superior structural preservation in protein shrinking tasks.", "questions": "Refer to Weaknesses", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1. The paper extends diffusion models to discrete, length-varying domains, a major conceptual leap beyond standard fixed-length sequence models. The application to protein shrinking which is previously dominated by self-supervised or autoregressive models is novel and impactful.\n2. The theoretical foundation is rigorous, derivations are mathematically sound. Experimental validation is multifaceted, spanning sequence likelihoods, structure preservation, and biological realism.", "weaknesses": "1. Basically, this work simply apply masked diffusion to protine domain. And the loss function designed is similar to the loss designed in [1]. It seems this work only extend the loss to the protein shrinking setting (as well as Theorem 4.2). This work should further elaborate what new insights does this paper convey.\n2. Effects of major components (e.g., π distribution, alignment weighting) is not sysytematically isolated. For example, if π is selected from other priors with a distribution shift, will there be a negative influence? By comparison with a unifrom weighting, is there evidence that the event intensity weighting improves stability or convergence?\n3. Section 4.2 acknowledges a distribution shift between training on noisy inserted sequences and sampling deletions from realistic proteins. Is there a way to conduct quantitative analysis of this mismatch?\n4. Hyperparameters are briefly mentioned, but full training details (compute hours, dataset splits) are incomplete.\n\n[1] Why masking diffusion works: Condition on the jump schedule for improved discrete diffusion.", "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": "Up3AqUw8YO", "reviewer": "Reviewer_gx5L", "summary": "The paper proposes SCISOR, a discrete diffusion model for shortening proteins by learning to delete residues. The forward process is insertion-only; the reverse denoiser learns to plan deletions that yield sequences resembling natural proteins. A dynamic-programming alignment counting algorithm marginalizes over insertion paths and produces a tractable training objective. Empirically, SCISOR is a competitive protein generative model, achieves SOTA deletion effect prediction on ProteinGym, and, when shrinking real proteins, better preserves predicted foldability and functional motifs than strong baselines. Code and additional analyses are provided.", "questions": "1. Would it be possible to include residue-level functional analyses for larger deletions—for example, checking whether annotated catalytic, binding, or interface residues are retained after shrinking, and whether their local structural geometry is preserved?\n2. Are there examples where the model maintains good global pLDDT/TM-score but loses key functional residues or pocket geometry? Showing a few such cases would help clarify the limits of the method and when shrinking becomes unsafe.\n3. The number of inference steps scales with the number of planned deletions. When would this becomes an issue in practice, i.e., what's the computational cost comparison of different methods in terms of different protein length and deletion length?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Clear, principled formulation of deletion-learning diffusion. The insertion-only forward / deletion reverse construction is elegant and purpose-built for length reduction, and it is distinct from prior substitution-only diffusion models in sequence generation. \n2. Strong deletion-specific evidence. SCISOR reaches SOTA on ProteinGym deletion effect prediction and shows consistent wins in structure/motif preservation during shrinking.  \n4. Useful case study and qualitative analyses. The RalA example and the comparison to deletions observed in natural alignments help interpret what the model is deleting. \n5. Implementation details, ablations, and code release are documented.", "weaknesses": "1. **Practical claim (“preserve function while shrinking”) is only partially supported.** \nEvidence for function preservation relies mainly on (i) ProteinGym deletion assays, which typically remove very few sites per sequence, and (ii) structure-centric proxies (pLDDT/TM/RMSD) for larger shrinkage experiments. These are helpful signals but do not fully validate functional retention at scale. The paper does measure functional-site enrichment, which is a step in the right direction, but this is confined to annotated motifs and could be expanded. Overall, the story is stronger on “planning deletions” than on “confirmed function after large deletions.” \n\n2. **Evaluation granularity for shrinking could be deepened.** \nFor the 200-sequence study, instead of global pLDDT/TM/RMSD curves, more  function-proximal evidence could also be considered in the main paper: e.g., family-stratified analysis of active site/binding pocket conservation, ligand-contact residue retention, or catalytic triad/metal-coordination integrity. \n\n3. **Distribution shift between training noise and inference use-case.** \nThe model is trained to reverse insertions into natural sequences, whereas shrinking deletes from a real protein directly. While the authors acknowledge limitations and future directions; some empirical evidence on the robustness would be helpful (e.g., proteins with long disordered tails vs compact cores)\n\n4. **Compute at inference scales with deletion count.** \nThe paper discusses efficient sampling, but more wall-clock comparisons against strong non-diffusion baselines (e.g., ProGen2-based pruning strategies) on long proteins would clarify practicality.", "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)