Pith. sign in

REVIEW 2 major objections 4 minor 1 cited by

What Exactly Does Guidance Do in Masked Discrete Diffusion Models

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For masked discrete diffusion with perfect scores, classifier-free guidance has explicit closed-form sampling formulas, and in one dimension the guided sampler returns the tilted distribution exactly.

desk verdict Real contribution with a fixable proof gap in the headline 2D asymptotic—send it out, require the fix. read the letter →

arxiv 2506.10971 v1 pith:NWSDMDYS submitted 2025-06-12 stat.ML cs.LG

He Ye , Rojas Kevin , Tao Molei This is my paper
classification stat.MLcs.LG MSC 60J2762B1068T07
keywords maskeddiscretediffusionclassifier-freeguidanceconcretescorecontinuous-timeMarkovchaintilteddistributiontotalvariationdecayabsorbingstrength
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks what classifier-free guidance actually does to the sampling distribution and the reverse dynamics of masked discrete diffusion models, and answers with closed-form solutions. In one dimension, with exact concrete scores and continuous-time integration, the guided reverse process at time $t$ is $q_t^{z,w}(x)=(1-((1-e^{-(T-t)})/(1-e^{-T}))^{Z})p^{z,w}(x)$ for $x=1,\dots,N-1$ and the remaining mass on the mask state, so at the end of sampling it returns exactly the tilted distribution $p^{z,w}(x)\propto p(x)^{-w}p(x|z)^{1+w}$. In two dimensions the same dynamics do not sample the tilted distribution; the final distribution carries the extra factor $(1/c_{x_1}+1/d_{x_2})/(1/c_N+1/d_N)$ multiplying $p^{z,w}(x)$. For large guidance strength $w$, the total-variation distance along the reverse trajectory decays at a rate exponential in $w$ in both dimensions, i.e., double-exponential in $w$, which explains why large guidance makes numerical integration stiff and unstable.

What carries the argument

The load-bearing object is the guided reverse transition rate matrix $\hat{Q}^{z,w}_t$ of Eq. (10), built from the unguided reverse rate $\bar{Q}_t$ and the class-conditional reverse rate $\bar{Q}^z_t$ by taking off-diagonal entries $\bar{Q}_t(y,x)^{-w}\bar{Q}^z_t(y,x)^{1+w}$. Because the absorbing forward process with $\sigma(t)\equiv1$ has analytic marginals (Proposition 3.1), every reverse rate is an explicit rational expression in $p$ and $p(\cdot|z)$ (Proposition 3.2). In $D=1$ the guided matrix is $Z\bar{Q}_t[p^{z,w}]$, a scaled reverse generator for the tilted distribution, and its one nontrivial eigenvalue gives the closed form of Theorem 4.1. In $D=2$ the matrix is block upper triangular; the proof diagonalizes it blockwise, producing eigenvalues $-c_i$, $-d_j$, and $-\lambda^{z,w}_{N,N}$, and the reciprocals of these eigenvalues appear directly in the density formula of Theorem 4.2. All dependence on the guidance strength enters through the normalizing constant $Z$ and the marginal ratios $c,d$.

What would settle it

Use analytic concrete scores drawn from a known mixture distribution, simulate the continuous-time reverse dynamics by uniformization or Gillespie down to negligible error, and compare the empirical distribution at $t=T$ with the explicit $q_T^{z,w}$ formulas. In 1D, a persistent mismatch that does not shrink as discretization error is reduced contradicts Theorem 4.1; in 2D, observing the empirical ratio $q_T^{z,w}(x)/p^{z,w}(x)$ to be constant across $x$ contradicts the predicted marginal-dependent ratio $(1/c_{x_1}+1/d_{x_2})/(1/c_N+1/d_N)$.

Watch

Extended reading notes

Core claim

The central claim is that the CFG reverse dynamics of a masked discrete diffusion has an explicit solution whenever concrete scores are exact and the reverse equation is integrated exactly. In $D=1$, Theorem 4.1 gives $q_t^{z,w}(x)=(1-((1-e^{-(T-t)})/(1-e^{-T}))^{Z})p^{z,w}(x)$ for $x=1,\dots,N-1$ and $q_t^{z,w}(N)=((1-e^{-(T-t)})/(1-e^{-T}))^{Z}$, where $Z=\sum_{x=1}^{N-1}p(x)^{-w}p(x|z)^{1+w}$; consequently the total-variation distance equals $((1-e^{-(T-t)})/(1-e^{-T}))^{Z}$, and $Z=\exp(wD_{1+w}(p(\cdot|z)\|p))$ grows like $\exp(\Theta(w))$ for $w\gg1$. In $D=2$, Theorem 4.2 gives an explicit but different solution, whose sampled distribution is $q_T^{z,w}(x)=((1/c_{x_1}+1/d_{x_2})/(1/c_N+1/d_N))p^{z,w}(x)$ on $\{1,\dots,N-1\}^2$, so the tilted distribution is not reached. The same double-exponential-in-$w$ total-variation decay holds in both dimensions for $w\gg1$. For class-mixture data, guidance amplifies class-private regions and suppresses overlap with other classes, and in $D=1$ the transformation to the private region preserves local mean and covariance of the class distribution.

Load-bearing premise

The derivation assumes the concrete scores are exact and the reverse process is integrated exactly in continuous time, so the closed forms describe an idealized sampler, not a finite-step trained model.

Editorial extensions

If this is right

  • In 1D masked diffusion with CFG, perfect scores and continuous-time integration imply the final samples exactly follow the tilted distribution $p^{z,w}$, so guidance changes the output distribution in a fully controlled way.
  • In 2D the sampled distribution deviates from $p^{z,w}$ by the marginal-dependent factor $(1/c_{x_1}+1/d_{x_2})/(1/c_N+1/d_N)$, so guidance's effect is not reducible to a single normalizing constant.
  • Under a class-mixture model, increasing $w$ shifts probability mass out of regions shared with other classes and into class-private regions, with support contained in the private region as $w\to\infty$.
  • For $w\gg1$, the TV distance along the reverse path decays roughly like $\exp(-\exp(\Theta(w))\ln((1-e^{-T})/(1-e^{-(T-t)})))$, making the sampling trajectory develop a very sharp transition in time and explaining why large guidance is numerically difficult.
  • In 1D, guidance preserves the local mean and covariance of the class distribution on the private region for every $w$, so the private mode keeps its shape while its weight changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper's claims: the exact 1D result makes masked-discrete CFG a rare exactly solvable guidance model, so it can serve as a testbed for separating score error from discretization error in guidance.
  • Beyond the paper's claims: because the 2D correction depends only on coordinate marginals through $c_{x_1}$ and $d_{x_2}$, a natural extension is to test whether higher-dimensional guided samplers reweight by sums over coordinate-marginal ratios, which would connect to the paper's conjecture that more private regions receive larger weights.
  • Beyond the paper's claims: the double-exponential-in-$w$ decay predicts a practical ceiling on guidance strength set by the integrator, so one could estimate a critical $w_*(\epsilon)$ at which the sharp transition is unresolved, and check whether it matches the empirical flattening in the paper's Figures 1c and 2c.
  • Beyond the paper's claims: the explicit solutions let one construct a discretization-error diagnostic, namely simulate the closed-form trajectory with a coarse integrator and compare against the analytic $q_t^{z,w}$, which isolates how much of the large-$w$ TV deviation is a numerical artifact rather than a modeling effect.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This paper analyzes classifier-free guidance (CFG) for masked discrete diffusion models under the idealization of exact concrete scores and no numerical integration error (Section 2.2). The authors derive explicit solutions for the guided reverse dynamics: in 1D, the time-t density is given by Theorem 4.1 and the terminal distribution is exactly the tilted distribution p^{z,w}; in 2D, the terminal distribution is the explicit formula in Remark 4.3, which deviates from p^{z,w}. They further prove that the total-variation distance between the time-t law and the terminal law decays at a rate double-exponential in the guidance strength w for large w (Propositions 4.1 and 4.4). Numerical experiments with trained models and with exact score evaluations illustrate the geometric effects of guidance and its impact on convergence.

Significance. The paper provides the first explicit closed-form analysis of CFG in masked discrete diffusion, a topic with mostly empirical studies so far. The 2D blockwise diagonalization in Appendix D and the exact-score verification in Appendix D.2 are substantive and give the community concrete formulas for the sampled distribution and convergence rate. The central idealization (exact scores, exact integration) is stated clearly, and the corresponding limitation for trained models is acknowledged; the empirical deviations for large w in Figures 1c and 2c are attributed to discretization. If the asymptotic proof issue identified below is fixed, the double-exponential decay claim is likely correct and constitutes a useful, falsifiable prediction about the sharp transition in the sampling dynamics.

major comments (2)
  1. [Appendix D.1] In the proof of Proposition 4.4, after deriving ln c_{x1} = Θ(w) and ln(-λ) = Θ(w), the authors state "we have c*_{x1} = Θ(w), c'_{x1} = Θ(w)". Under the definition of Θ in Section 2.1 (linear growth), this implication is false: log c = Θ(w) implies c = exp(Θ(w)), not c = Θ(w). If the literal statement were used in the bound -(1/c*) r^{c*}(1/c* - ln r), the resulting TV would decay like exp(-Θ(w) ln(1/r)), which is only single-exponential in w. This is load-bearing because Proposition 4.4 is the headline 2D convergence-rate result. The claim is likely salvageable by writing c* = exp(Θ(w)) and tracking the exp(±Θ(w)) prefactors from Z, 1/c*, and 1/(-λ), which yields -ln TV = exp(Θ(w)) ln(1/r)(1+o(1)), but the printed proof needs this correction.
  2. [Appendix D.1] In the final display of the same proof, the equation TV = exp(Θ(w)) exp(-Θ(w)) r^{exp(Θ(w))} + r^{exp(Θ(w))} treats exp(Θ(w))·exp(-Θ(w)) as an exp(O(1)) prefactor, which is not justified by the Θ notation because the two Θ(w)'s may have different constants. The same fix as in the previous comment—keeping track of explicit constants or using a sharper asymptotic notation—is required before the double-exponential statement follows.
minor comments (4)
  1. [Section 5, Figure 2c] Figure 2c shows only the empirical TV for the 2D case and does not overlay the theoretical reference curve, unlike Figure 1c for the 1D case; adding the theoretical curve would make the comparison quantitative.
  2. [Section 2.2, Eq. (5)] The reverse dynamics in Eq. (2) starts at p_T, while the approximate dynamics in Eq. (5) starts at the point mass δ_[M]; Remark 3.1 explains that there is no initialization error in this model, but it would be clearer to state this immediately after Eq. (5).
  3. [Remark 4.1] The phrase "the exponential decay rate of TV is exponential in w" is potentially confusing; a more precise statement is that -ln TV grows exponentially in w for fixed t and T.
  4. [Proposition 4.3] The displayed block matrices for \gL^{z,w}_i and \gM^{z,w} contain alignment issues with stray ellipses and zeros; a cleaner typesetting would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's explicit solutions follow from exact-score ODE analysis with no fitted parameter relabeled as a prediction.

full rationale

The derivation chain is self-contained rather than circular. After stating the idealization of exact concrete scores and continuous-time integration (Section 2.2), the paper derives the unguided reverse densities from the explicit eigendecomposition of the absorbing rate matrix (Proposition 3.1, Theorem 3.1), then treats the CFG rate matrix (10) as a new object and diagonalizes it (Theorem 4.2 and Appendix D). The 1D identification that the CFG rate matrix equals Z times the reverse rate of the tilted distribution is a computed equivalence verified from the concrete-score formulas, not a definition of CFG in terms of the tilted distribution; the tilted distribution p^{z,w} is introduced independently in Eq. (6) as an intuitive target, while the actual guided process is defined by Nisonoff et al.'s rate-matrix construction in Eqs. (9)-(10). The 2D results, including the explicit density formula and the double-exponential TV-rate statement, come from a blockwise eigenvalue decomposition with no fitted parameter being relabeled as a prediction. The only self-citation (Guo et al., 2024) appears in the related-work appendix and is not load-bearing. The stated idealizations (exact scores, σ(t)≡1) are explicit assumptions, and the observed mismatch for large w is attributed by the authors to Tau-leaping discretization rather than silently baked into the theory. The alleged Θ(w) versus exp(Θ(w)) slip in the proof of Proposition 4.4, if present, is a correctness issue about asymptotic notation, not a circular-dependence issue.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim is an explicit solution of a fixed Markov process; it introduces no free parameters and no invented entities. All inputs are the standard absorbing diffusion matrix, the Nisonoff et al. CFG rule, the mixture assumption, and the exact-score/no-discretization idealization, all of which are stated in the paper.

assumptions (6)
  • domain assumption The forward process is the absorbing (mask) process with constant rate: Q_t = σ(t) Q with σ(t)≡1 (Eq. 11).
    All explicit time-dependence (e.g., e^{-t} factors in Proposition 3.1 and the r(t) terms in Theorems 4.1 and 4.2) relies on this constant-rate choice.
  • domain assumption The guided reverse rate is defined by the Nisonoff et al. tilting rule: \hat{Q}^{z,w}_t(y,x) = \bar{Q}_t(y,x)^{-w} \bar{Q}^z_t(y,x)^{1+w} (Eq. 10).
    The paper analyzes this specific guidance rule; the conclusions about sampled distributions and TV decay describe this process, not alternative discrete CFG formulations such as Sahoo et al.'s.
  • domain assumption The data distribution is a mixture of class distributions with weights a_k (Assumption 1.1).
    The support-geometry results (Propositions 4.2 and 4.5) and the claims about amplification of class-specific regions require this mixture structure.
  • domain assumption The data distribution has zero mass on the masked state(s), and the reverse process starts from the point mass at the masked state [M] (Eqs. 5 and 9).
    The formulas for q_t and the TV expressions assume p_{z,w}(N)=0 and q_0 = δ_[M].
  • domain assumption Exact concrete scores and exact continuous-time integration (Section 2.2).
    The derivation assumes no score approximation error and no discretization error; this is the paper's central idealization and is stated explicitly.
  • standard math Standard linear algebra and continuous-time Markov chain semigroup theory, including diagonalization of the rate matrices (Lemmas and Proofs in Appendices B-D).
    The proofs use matrix exponentials and eigen-decompositions; no nonstandard math is introduced.

how reviews work

0 comments
Cite this review

Pith. "Pith review of What Exactly Does Guidance Do in Masked Discrete Diffusion Models." pith.science (2026). https://pith.science/paper/NWSDMDYS

@misc{pith2026250610971,
  author       = {Pith},
  title        = {Pith review of: What Exactly Does Guidance Do in Masked Discrete Diffusion Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NWSDMDYS}},
  note         = {Machine review of arXiv:2506.10971}
}
abstract

We study masked discrete diffusion models with classifier-free guidance (CFG). Assuming no score error nor discretization error, we derive an explicit solution to the guided reverse dynamics, so that how guidance influences the sampling behavior can be precisely characterized. When the full data distribution is a mixture over classes and the goal is to sample from a specific class, guidance amplifies class-specific regions while suppresses regions shared with other classes. This effect depends on the guidance strength $w$ and induces distinct covariance structures in the sampled distribution. Notably, we observe quantitatively different behaviors in $1$D and $2$D. We also show that for large $w$, the decay rate of the total variation ($\mathrm{TV}$) along the reverse dynamics is double-exponential in $w$ for both $1$D and $2$D. These findings highlight the role of guidance, not just in shaping the output distribution, but also in controlling the dynamics of the sampling trajectory. Our theoretical analysis is supported by experiments that illustrate the geometric effects of guidance and its impact on convergence.

Figures

Figures reproduced from arXiv: 2506.10971 by the authors.

Figure 1
Figure 1. In the first two plots, we illustrate how the effect of guidance differs depending on whether the class [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. In the first two plots, we illustrate how the effect of guidance differs depending on whether the class [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. heat maps for p(·|z1), p(·|z2) and p. of privacy based on our formulas. As shown in [PITH_FULL_IMAGE:figures/full_fig_p027_3.png] view at source ↗
Figures from the paper (20 more)
Figure 4
Figure 4. Figure 4: identification of different regions. w → ∞. We have A z1,∞ 1 = 2, Az1,∞ 2,1 = 1x1=1, Az1,∞ 2,2 = 1x2=1, Az1,∞ 4 = 0. Therefore, the sampled distribution q z1,∞ T (·|z1) adapts p(·|z1) by putting these weights on the 4 regions 27 [PITH_FULL_IMAGE:figures/full_fig_p027_4.png]
Figure 5
Figure 5. Figure 5: distributions under different guidance strengths: [PITH_FULL_IMAGE:figures/full_fig_p029_5.png]
Figure 6
Figure 6. Figure 6: Histograms corresponding to the disjoint example. [PITH_FULL_IMAGE:figures/full_fig_p030_6.png]
Figure 7
Figure 7. Figure 7: Histograms corresponding to the intersection example. [PITH_FULL_IMAGE:figures/full_fig_p030_7.png]
Figure 8
Figure 8. Figure 8: Heat plot corresponding to the disjoint example. [PITH_FULL_IMAGE:figures/full_fig_p031_8.png]
Figure 9
Figure 9. Figure 9: Heat plot corresponding to the intersection example. [PITH_FULL_IMAGE:figures/full_fig_p031_9.png]
Figure 10
Figure 10. Figure 10: Class 0 32 [PITH_FULL_IMAGE:figures/full_fig_p032_10.png]
Figure 11
Figure 11. Figure 11: Class 1 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0 1 2 3 Dime…
Figure 12
Figure 12. Figure 12: Class 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0 1 2 3 Dime…
Figure 13
Figure 13. Figure 13: Unconditional Generation 33 [PITH_FULL_IMAGE:figures/full_fig_p033_13.png]
Figure 14
Figure 14. Figure 14: Class 0 with w = 1 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0…
Figure 15
Figure 15. Figure 15: Class 1 with w = 1 34 [PITH_FULL_IMAGE:figures/full_fig_p034_15.png]
Figure 16
Figure 16. Figure 16: Class 2 with w = 1 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0…
Figure 17
Figure 17. Figure 17: Unconditional Generation with w = 1 35 [PITH_FULL_IMAGE:figures/full_fig_p035_17.png]
Figure 18
Figure 18. Figure 18: Class 0 with w = 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0…
Figure 19
Figure 19. Figure 19: Class 1 with w = 3 36 [PITH_FULL_IMAGE:figures/full_fig_p036_19.png]
Figure 20
Figure 20. Figure 20: Class 2 with w = 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 2 Dims 1 vs 2 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 3 Dims 1 vs 3 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 4 Dims 1 vs 4 2 0 2 Dimension 1 3 2 1 0 1 2 3 Dimension 5 Dims 1 vs 5 2 0 2 Dimension 2 3 2 1 0…
Figure 21
Figure 21. Figure 21: Unconditional Generation with w = 3 37 [PITH_FULL_IMAGE:figures/full_fig_p037_21.png]
Figure 22
Figure 22. Figure 22: Applying guidance reduces the are of intersection between classes. Notice how number [PITH_FULL_IMAGE:figures/full_fig_p038_22.png]
Figure 23
Figure 23. Figure 23: Applying guidance reduces the area of intersection between classes. Notice how number [PITH_FULL_IMAGE:figures/full_fig_p039_23.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Discrete Diffusion Models: A Unified Framework from Tokenization to Generation

    cs.LG 2026-07 unverdicted novelty 4.0 of 10

    Discrete diffusion models are re-framed as instances of a tokenization-centric, four-component design space (corruption, denoiser, objective, sampler) in a broad survey with no new experimental or theoretical results.

Reference graph

Works this paper leans on

33 extracted references · 21 canonical work pages · cited by 1 Pith paper

  1. [1]

    Austin, D

    J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and R. Van Den Berg. Structured denoising diffusion models in discrete state-spaces. Advances in neural information processing systems, 34: 0 17981--17993, 2021

    work page 2021

  2. [2]

    F. Bao, S. Nie, K. Xue, Y. Cao, C. Li, H. Su, and J. Zhu. All are worth words: A vit backbone for diffusion models. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 22669--22679, 2023

    work page 2023

  3. [3]

    Bradley and P

    A. Bradley and P. Nakkiran. Classifier-free guidance is a predictor-corrector. arXiv preprint arXiv:2408.09000, 2024

    arXiv 2024

  4. [4]

    Campbell, J

    A. Campbell, J. Benton, V. De Bortoli, T. Rainforth, G. Deligiannidis, and A. Doucet. A continuous time framework for discrete denoising models. Advances in Neural Information Processing Systems, 35: 0 28266--28279, 2022

    work page 2022

  5. [5]

    Chen and L

    H. Chen and L. Ying. Convergence analysis of discrete diffusion model: Exact implementation through uniformization. arXiv preprint arXiv:2402.08095, 2024

    arXiv 2024

  6. [6]

    Chidambaram, K

    M. Chidambaram, K. Gatmiry, S. Chen, H. Lee, and J. Lu. What does guidance do? a fine-grained analysis in a simple setting. arXiv preprint arXiv:2409.13074, 2024

    arXiv 2024

  7. [7]

    Dhariwal and A

    P. Dhariwal and A. Nichol. Diffusion models beat gans on image synthesis. Advances in neural information processing systems, 34: 0 8780--8794, 2021

    work page 2021

  8. [8]

    D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of computational physics, 22 0 (4): 0 403--434, 1976

    work page 1976

Show all 33 references
  1. [9]

    D. T. Gillespie. Approximate accelerated stochastic simulation of chemically reacting systems. The Journal of chemical physics, 115 0 (4): 0 1716--1733, 2001

    2001

  2. [10]

    W. K. Grassmann. Transient solutions in markovian queueing systems. Computers & Operations Research, 4 0 (1): 0 47--53, 1977

    1977

  3. [11]

    Gruver, S

    N. Gruver, S. Stanton, N. Frey, T. G. Rudner, I. Hotzel, J. Lafrance-Vanasse, A. Rajpal, K. Cho, and A. G. Wilson. Protein design with guided discrete diffusion. Advances in neural information processing systems, 36: 0 12489--12517, 2023

    2023

  4. [12]

    W. Guo, Y. Zhu, M. Tao, and Y. Chen. Plug-and-play controllable generation for discrete masked models. arXiv preprint arXiv:2410.02143, 2024

    2024 arXiv

  5. [13]

    X. Han, S. Kumar, and Y. Tsvetkov. Ssd-lm: Semi-autoregressive simplex-based diffusion language model for text generation and modular control. arXiv preprint arXiv:2210.17432, 2022

    2022 arXiv

  6. [14]

    Ho and T

    J. Ho and T. Salimans. Classifier-free diffusion guidance. In NeurIPS 2021 Workshop on Deep Generative Models and Downstream Applications, 2021

    2021

  7. [15]

    J. Ho, A. Jain, and P. Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33: 0 6840--6851, 2020

    2020

  8. [16]

    J. Ho, T. Salimans, A. Gritsenko, W. Chan, M. Norouzi, and D. J. Fleet. Video diffusion models. Advances in Neural Information Processing Systems, 35: 0 8633--8646, 2022

    2022

  9. [17]

    Huang, L

    H. Huang, L. Sun, B. Du, and W. Lv. Conditional diffusion based on discrete graph structures for molecular graph generation. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pages 4302--4311, 2023

    2023

  10. [18]

    Z. Kong, W. Ping, J. Huang, K. Zhao, and B. Catanzaro. Diffwave: A versatile diffusion model for audio synthesis. In International Conference on Learning Representations, 2021

    2021

  11. [19]

    X. Li, J. Thickstun, I. Gulrajani, P. S. Liang, and T. B. Hashimoto. Diffusion-lm improves controllable text generation. Advances in neural information processing systems, 35: 0 4328--4343, 2022

    2022

  12. [20]

    A. Lou, C. Meng, and S. Ermon. Discrete diffusion modeling by estimating the ratios of the data distribution. arXiv preprint arXiv:2310.16834, 2023

    2023 arXiv

  13. [21]

    Lovelace, V

    J. Lovelace, V. Kishore, C. Wan, E. Shekhtman, and K. Q. Weinberger. Latent diffusion for language generation. Advances in Neural Information Processing Systems, 36: 0 56998--57025, 2023

    2023

  14. [22]

    C. Meng, K. Choi, J. Song, and S. Ermon. Concrete score matching: Generalized score matching for discrete data. Advances in Neural Information Processing Systems, 35: 0 34532--34545, 2022

    2022

  15. [23]

    A. Q. Nichol, P. Dhariwal, A. Ramesh, P. Shyam, P. Mishkin, B. Mcgrew, I. Sutskever, and M. Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. In International Conference on Machine Learning, pages 16784--16804. PMLR, 2022

    2022

  16. [24]

    S. Nie, F. Zhu, Z. You, X. Zhang, J. Ou, J. Hu, J. ZHOU, Y. Lin, J.-R. Wen, and C. Li. Large language diffusion models. In ICLR 2025 Workshop on Deep Generative Model in Machine Learning: Theory, Principle and Efficacy

    2025

  17. [25]

    Nisonoff, J

    H. Nisonoff, J. Xiong, S. Allenspach, and J. Listgarten. Unlocking guidance for discrete state-space diffusion and flow models. arXiv preprint arXiv:2406.01572, 2024

    2024 arXiv

  18. [26]

    J. Ou, S. Nie, K. Xue, F. Zhu, J. Sun, Z. Li, and C. Li. Your absorbing discrete diffusion secretly models the conditional distributions of clean data. arXiv preprint arXiv:2406.03736, 2024

    2024 arXiv

  19. [27]

    Saharia, W

    C. Saharia, W. Chan, S. Saxena, L. Li, J. Whang, E. L. Denton, K. Ghasemipour, R. Gontijo Lopes, B. Karagol Ayan, T. Salimans, et al. Photorealistic text-to-image diffusion models with deep language understanding. Advances in neural information processing systems, 35: 0 36479-...

    2022

  20. [28]

    Sahoo, M

    S. Sahoo, M. Arriola, Y. Schiff, A. Gokaslan, E. Marroquin, J. Chiu, A. Rush, and V. Kuleshov. Simple and effective masked diffusion language models. Advances in Neural Information Processing Systems, 37: 0 130136--130184, 2024

    2024

  21. [29]

    J. Shi, K. Han, Z. Wang, A. Doucet, and M. K. Titsias. Simplified and generalized masked diffusion for discrete data. NeurIPS, 2024

    2024

  22. [30]

    Y. Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, and B. Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021

    2021

  23. [31]

    Stark, B

    H. Stark, B. Jing, C. Wang, G. Corso, B. Berger, R. Barzilay, and T. Jaakkola. Dirichlet flow matching with applications to dna sequence design. arXiv preprint arXiv:2402.05841, 2024

    2024 arXiv

  24. [32]

    Y. Wu, M. Chen, Z. Li, M. Wang, and Y. Wei. Theoretical insights for diffusion guidance: A case study for gaussian mixture models. arXiv preprint arXiv:2403.01639, 2024

    2024 arXiv

  25. [33]

    Xiong, H

    J. Xiong, H. Nisonoff, I. Gaur, and J. Listgarten. Guide your favorite protein sequence generative model. arXiv preprint arXiv:2505.04823, 2025

    2025

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.