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REVIEW 3 major objections 5 minor 21 references

Distilling electrostatic generative models reduces to matching two electrostatic fields, and the resulting few-step generators match or beat their teachers.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 14:51 UTC pith:TQMTI2QP

load-bearing objection A genuinely new distillation objective for PFGM++ that reduces to SiD at D→∞; the theory has an ideal-limit gap and the empirical support lacks error bars, but the contribution is real and refereeable. the 3 major comments →

arxiv 2509.22454 v2 pith:TQMTI2QP submitted 2025-09-26 cs.LG

Overclocking Electrostatic Generative Models

Daniil Shlenskii , Alexander Korotin This is my paper
classification cs.LG
keywords Inverse Poisson Flow MatchingdistillationPFGM++electrostatic generative modelsscore identity distillationfew-step generationminimax optimizationgenerative modeling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper introduces Inverse Poisson Flow Matching (IPFM), a distillation method that turns the slow ODE-based sampling of PFGM++ electrostatic generative models into one-to-four-step generators. Distillation is framed as an inverse problem: find a generator whose induced electrostatic field matches the field of a trained teacher. The authors prove that this constrained problem is equivalent to a tractable minimax objective, and show that in the diffusion limit (D approaching infinity) the method recovers Score Identity Distillation. On CIFAR-10 and FFHQ 64x64, distilled generators match or beat their teachers in a handful of steps — e.g., a 4-step CIFAR-10 generator reaches FID 1.75 versus the teacher's 1.92, and a 2-step FFHQ generator reaches 1.72 versus 2.43. The paper also reports faster convergence for finite auxiliary dimension D than in the diffusion limit.

Core claim

The central claim is that distilling an electrostatic generative model reduces to matching the electrostatic field induced by the generator's output distribution to the field of the teacher. The paper formalizes this as the Inverse Poisson Flow Matching problem and proves (Theorem 3.2) that it is equivalent to an unconstrained minimax objective: the generator minimizes the expected squared difference between the teacher denoiser and a student denoiser trained on the generator's own samples. This reformulation is what makes the distillation practical. As D approaches infinity, the objective asymptotically equals the Score Identity Distillation objective up to a known term, which lets the auth

What carries the argument

The key mechanism is the minimax objective of Theorem 3.2, which replaces the intractable inner arg-min over the student field with a maximum over student denoisers trained on the generator's distribution. The identity that makes this work is an algebraic rewriting of the field-matching loss: for any positive weighting, the field-matching error equals the expected teacher denoising loss minus the expected student denoising loss. The second component is the reparameterization r = σ√D connecting PFGM++ to diffusion, which allows SiD's hyperparameters and regularization to be ported to finite D.

Load-bearing premise

The proof that the minimax objective is equivalent to field matching assumes the student denoiser reaches its global minimum and that a generator distribution exists whose induced field exactly matches the teacher's; in practice only alternating gradient updates are run, so the equivalence holds only in the ideal optimization limit.

What would settle it

A controlled comparison on a single architecture and dataset where the D→∞ IPFM run does not reproduce SiD's reported one-step FID (or where finite-D convergence is slower than D→∞ when compute is matched) would undercut the core equivalence and the finite-D advantage claim.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • PFGM++ models can be accelerated from tens of neural network evaluations to 1–4 without losing quality; in several configurations the distilled generator outperforms its teacher.
  • The D→∞ limit of IPFM is essentially SiD, giving a theoretical bridge between electrostatic distillation and diffusion distillation.
  • Finite auxiliary dimension D converges faster during distillation than the diffusion limit, supporting the claim that finite-D electrostatic models have favorable optimization geometry.
  • SiD-inspired regularization (α=1.0) improves both convergence speed and final FID across all tested D.
  • The same inverse-field-matching recipe may extend to other flow-based generative models whose dynamics are defined by an estimated field or score.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If finite-D convergence advantages hold beyond the two datasets tested, the practical recommendation for distillation would be to prefer moderate D values over the D→∞ diffusion limit, the opposite of the usual convenience of reusing diffusion infrastructure.
  • The minimax equivalence assumes the inner student field reaches its global optimum; in practice alternating gradient updates mean the theoretical equivalence holds only approximately, so the gap between the two might show up as sensitivity to the student learning rate or batch size.
  • The connection to SiD suggests IPFM could inherit SiD's known instabilities at high regularization α; the paper indeed reports divergence at α=1.2 with certain architectures, which may reflect the same phenomenon.
  • A natural testable extension would be applying IPFM to distill other electrostatic or physics-inspired generative models, such as field matching for data-to-data translation, where the same field-matching inverse problem appears.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper introduces Inverse Poisson Flow Matching (IPFM), a distillation method for PFGM++ electrostatic generative models. The idea is to train a generator whose induced electrostatic field matches the teacher field, formulated as a constrained inverse problem (Definition 3.1), then reformulated as a tractable minimax objective (Theorem 3.2, Proposition 3.3). The authors show that in the D→∞ limit the objective reduces, up to an algebraic identity, to Score Identity Distillation (SiD), and transfer SiD's regularization to finite D. Experiments on CIFAR-10 and FFHQ 64x64 report few-step FID scores that match or surpass the teacher PFGM++ models, with faster convergence for finite D than in the diffusion limit (Figure 2, Table 1). The main contributions are claimed as a principled distillation framework for all D and a theoretical connection to SiD.

Significance. If the theoretical equivalence and empirical results hold, IPFM is a useful contribution: it extends score-distillation ideas to the full PFGM++ family and suggests finite-D electrostatics are particularly amenable to distillation. The paper is self-contained: the derivations in Appendix A are algebraically sound under ideal optimization assumptions, Proposition 3.4 is an exact identity, and hyperparameters are inherited from prior work rather than tuned to the reported numbers. The empirical FID improvements over the teacher (e.g., 4-step CIFAR-10 FID 1.75 with D=128, α=1.0 vs teacher 1.92) are plausible and align with prior evidence on finite-D robustness. However, the central theorem is an ideal-limit statement whose assumptions are not stated precisely and are not satisfied by the practical algorithm; this weakens the theoretical justification. The empirical claims about convergence also lack statistical support. These issues are fixable without changing the core method.

major comments (3)
  1. [Appendix A, Eq. (29)-(35); Theorem 3.2] The proof introduces a positive weighting λ(r) into the main functional by arguing that it 'does not change the optimum value (which equals 0)'. This is valid only if a generator distribution exists whose induced field exactly matches the teacher's. For finite-capacity networks and finite data, the minimal field discrepancy is generally positive, and the minimizers of E||fψ−f*||² and E λ(r)||fψ−f*||² can differ when the zero optimum is not attained. Thus the claimed equivalence 'for any positive weighting function λ(r)>0' does not follow in the practically relevant non-attainable case. This is load-bearing because Algorithm 1 optimizes a weighted objective with a finite-capacity student and generator. The theorem should either explicitly assume attainability of the zero optimum, or provide a bound on the error introduced when the optimum is not zero.
  2. [Section 3.4, Algorithm 1, Eq. (37)] Theorem 3.2 states the equivalence for a weighting λ(r)>0 that depends only on the radial coordinate r. The practical objective in Algorithm 1 uses λ(σ)=C / ||ŷ*_φ(x_σ,σ)−y||_{1,sg}, which depends on the sampled data y and student input x_σ (and uses a stop-gradient). This weighting is not covered by the theorem. Moreover, Algorithm 1 replaces the inner maximization with a single gradient update rather than solving the inner problem to optimality. The paper should clarify the formal status of the practical objective: it is an approximation to the theoretical minimax objective, not a direct instance of it.
  3. [Section 4, Figure 2 and Table 1] The claim that IPFM converges faster for finite D than for D→∞ is based on individual FID curves without error bars, and Table 1 reports only the minimum of 3 FID evaluations without standard deviations or number of seeds. The observed differences between D=128, D=2048 and D=∞ in Table 1 are small (e.g., CIFAR-10 4-step α=1.0: 1.75 vs 1.82 vs 1.86), and the convergence speed claim rests on a visual comparison in Figure 2. Given that 'finite D converges faster' is a stated main finding, it needs statistical support or should be presented more cautiously.
minor comments (5)
  1. [Algorithm 2] The schedule σ_n = σ_init + (n−1)/N (σ_min − σ_init) for n=1,...,N−1 does not reach σ_min and appears inconsistent with the text's σ_N=σ_min. Please check the indexation.
  2. [Eq. (23)-(25), Proposition 3.4] The phrase 'closely recovers SiD' is imprecise: Eq. (25) shows L_IPFM^{D→∞} = 2L_SiD − E||ŷ*_φ − ŷ_ψ||². Since the extra term is part of the regularized objective, the connection is exact only after accounting for that term. Consider stating this explicitly in the main text.
  3. [Appendix B] The architecture names 'ncsn++' and 'ddpm++' appear without citations or explanation. A reader unfamiliar with Karras et al. (2022) will not know the difference; please add references or a brief description.
  4. [Algorithm 1] The initialization line 'θ←ϕ, ψ←ϕ' is ambiguous: θ is the generator, ψ the student denoiser, and ϕ the teacher. It is clear from context that all are initialized from the teacher weights, but the notation should be clarified.
  5. [Appendix B, Evaluation] Reporting the minimum of 3 FID evaluations is a favorable selection; please also report the mean and standard deviation, or at least justify the practice of taking the minimum.

Circularity Check

0 steps flagged

No circularity: IPFM's objective is an algebraic reformulation, the D→∞ SiD connection is an exact identity, and the empirical results are independent evaluations against the PFGM++ teacher.

full rationale

The derivation is self-contained. Definition 3.1 and Theorem 3.2 are connected by an explicit algebraic identity (Appendix A, Eqs. 31–35): for fixed θ, the student field is defined as the argmin of the Poisson-flow denoising loss, and the minimax objective is obtained by rewriting E||fψ−f*||² through that argmin; no fitted quantity is renamed as a prediction. The D→∞ reduction to SiD (Prop. 3.4, Eq. 25) is an exact expansion of ||ŷ*−y||²−||ŷψ−y||², not an imported or self-citational result. Hyperparameters (noise schedule, weighting, α=1.0) are inherited from prior work or chosen by ablation, and the headline FID numbers are independent evaluations against the PFGM++ teacher. The only caveat is mathematical, not circular: the proof of Theorem 3.2 assumes the ideal optimum value 0 is attained (Appendix A: 'since it does not change the optimum value (which equals 0)'), and the practical stochastic weighting in Eq. (37) is not literally a function of r alone; these are rigor gaps in the ideal-limit justification, but they do not make the derivation reduce to its own inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

Ledger: two free parameters chosen by hand (regularization alpha=1.0 from ablation, 30k-sample training budget from computational constraints); five domain assumptions inherited from PFGM++, the idealization of perfect field matching, the exact global optimality of the inner student step, the D to infinity limit relations, and the validity of transferred SiD hyperparameters at finite D; no invented entities.

free parameters (2)
  • Regularization strength alpha = 1.0
    Selected via ablation (Appendix B) as a stable balance across architectures and D; the headline outperform-teacher results use alpha=1.0.
  • Training budget = 30k generator samples
    Fixed due to computational constraints; used for all reported runs and affects the convergence-speed comparison between D values.
axioms (5)
  • domain assumption The PFGM++ perturbation kernel p_r(x_r|y) and the field-to-denoising relation f(x,r)=(x - y_hat(x,r))/(r/sqrt(D)) correctly describe the generative dynamics.
    Invoked in Section 2.2 and used throughout the IPFM objective (Eq. 21); taken from Xu et al. 2023.
  • domain assumption A generator distribution p_theta(y) exists whose induced electrostatic field equals the teacher field, making the outer optimum 0.
    Used in the proof of Theorem 3.2 (Appendix A) to justify adding the weighting lambda(r) without changing the optimum; idealized because the generator is finite-capacity.
  • domain assumption The inner minimization over psi attains the global optimum at each step.
    Theorem 3.2's equivalence relies on f_psi being the exact argmin; Algorithm 1 only takes one gradient step, so the practical objective is an approximation (Section 3.4).
  • domain assumption The D to infinity limit relations from PFGM++ (ODE, kernel, objective convergence) hold as stated.
    Used in Sections 2.3 and 3.2 to define the asymptotic IPFM objective and connect it to SiD.
  • domain assumption Transferred hyperparameters from SiD and Karras et al. (noise schedule, weighting) remain valid for finite D under r=sigma*sqrt(D).
    Stated in Appendix B as the adaptation recipe; empirically verified only on the two benchmark datasets.

pith-pipeline@v1.3.0-alltime-deepseek · 16404 in / 14679 out tokens · 109968 ms · 2026-08-04T14:51:49.526698+00:00 · methodology

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Cite this review

Pith. "Pith review of Overclocking Electrostatic Generative Models." pith.science (2026). https://pith.science/paper/TQMTI2QP

@misc{pith2026250922454,
  author       = {Pith},
  title        = {Pith review of: Overclocking Electrostatic Generative Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TQMTI2QP}},
  note         = {Machine review of arXiv:2509.22454}
}
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read the original abstract

Electrostatic generative models such as PFGM++ have recently emerged as a powerful framework, achieving competitive performance in image synthesis. PFGM++ operates in an extended data space with auxiliary dimensionality $D$, recovering the diffusion model framework as $D\to\infty$, while yielding superior empirical results for finite $D$. Like diffusion models, PFGM++ relies on expensive ODE simulations to generate samples, making it computationally costly. To address this, we propose Inverse Poisson Flow Matching (IPFM), a principled distillation framework that accelerates electrostatic generative models across all values of $D$. Our IPFM reformulates distillation as an inverse problem: learning a generator whose induced electrostatic field matches that of the teacher. We derive a tractable training objective for this problem and show that, as $D\to\infty$, our IPFM closely recovers Score Identity Distillation (SiD), a recent method for distilling diffusion models. Empirically, our IPFM produces distilled generators that achieve near-teacher or even superior sample quality using only a few function evaluations. Moreover, we find that one-step generator distillation converges faster at finite $D$ than in the $D\to\infty$ diffusion limit, aligning with prior evidence that finite-$D$ PFGM++ models offer more favorable optimization and sampling behavior.

Figures

Figures reproduced from arXiv: 2509.22454 by Alexander Korotin, Daniil Shlenskii.

Figure 1
Figure 1. Figure 1: Our IPFM overview. We seek a generator Gθ whose distribution pθ(y) induces an electrostatic field fψ that matches the field f ∗ ϕ of the teacher model trained on real data pdata(y). 1 INTRODUCTION Diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020; Song et al., 2020) have emerged as a leading paradigm in generative modeling, achieving state-of-the-art performance in synthesizing high-quality sa… view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of our IPFM. Plots show FID evolution during training (measured in thou￾sands of generator samples) for different IPFM settings. The gray horizontal band represents the range of final performance (minimum to maximum FID across different D) achieved by the original PFGM++ teacher models, providing a target quality threshold. distribution and the true data distribution, and (2) teacher models wit… view at source ↗
Figure 3
Figure 3. Figure 3: Samples generated with our IPFM (D=128,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Samples generated with our IPFM (D=128,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p017_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Samples generated with our IPFM (D=128,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Samples generated with our IPFM (D=128,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Samples generated with our IPFM (D=128,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Samples generated with our IPFM (D=128,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Samples generated with PFGM++ (D=128,NFE=5) teacher on CIFAR-10 (FID [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Samples generated with PFGM++ (D=128,NFE=9) teacher on CIFAR-10 (FID=37.79) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Samples generated with PFGM++ (D=128,NFE=17) teacher on CIFAR-10 (FID=3.32) [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Samples generated with PFGM++ (D=128,NFE=35) teacher on CIFAR-10 (FID=1.92) [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Samples generated with our IPFM (D=2048,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Samples generated with our IPFM (D=2048,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p018_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Samples generated with our IPFM (D=2048,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Samples generated with our IPFM (D=2048,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Samples generated with our IPFM (D=2048,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p019_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Samples generated with our IPFM (D=2048,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Samples generated with PFGM++ (D=2048,NFE=5) teacher on CIFAR-10 (FID [PITH_FULL_IMAGE:figures/full_fig_p019_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Samples generated with PFGM++ (D=2048,NFE=9) teacher on CIFAR-10 (FID=37.14) [PITH_FULL_IMAGE:figures/full_fig_p019_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Samples generated with PFGM++ (D=2048,NFE=17) teacher on CIFAR-10 (FID=3.37) [PITH_FULL_IMAGE:figures/full_fig_p019_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Samples generated with PFGM++ (D=2048,NFE=35) teacher on CIFAR-10 (FID=1.91) [PITH_FULL_IMAGE:figures/full_fig_p019_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Samples generated with our IPFM (D=inf,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p019_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Samples generated with our IPFM (D=inf,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p020_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Samples generated with our IPFM (D=inf,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p020_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Samples generated with our IPFM (D=inf,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p020_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Samples generated with our IPFM (D=inf,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p020_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Samples generated with our IPFM (D=inf,NFE=4, [PITH_FULL_IMAGE:figures/full_fig_p020_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Samples generated with PFGM++ (D=inf,NFE=5) teacher on CIFAR-10 (FID [PITH_FULL_IMAGE:figures/full_fig_p020_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Samples generated with PFGM++ (D=inf,NFE=9) teacher on CIFAR-10 (FID=40.24) [PITH_FULL_IMAGE:figures/full_fig_p020_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Samples generated with PFGM++ (D=inf,NFE=17) teacher on CIFAR-10 (FID=3.74) [PITH_FULL_IMAGE:figures/full_fig_p021_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Samples generated with PFGM++ (D=inf,NFE=35) teacher on CIFAR-10 (FID=1.98) [PITH_FULL_IMAGE:figures/full_fig_p021_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Samples generated with our IPFM (D=128,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p021_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: Samples generated with our IPFM (D=128,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p021_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Samples generated with our IPFM (D=128,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p021_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Samples generated with our IPFM (D=128,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p021_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Samples generated with PFGM++ (D=128,NFE=5) teacher on FFHQ 64x64 (FID [PITH_FULL_IMAGE:figures/full_fig_p021_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Samples generated with PFGM++ (D=128,NFE=13) teacher on FFHQ 64x64 [PITH_FULL_IMAGE:figures/full_fig_p022_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: Samples generated with PFGM++ (D=128,NFE=31) teacher on FFHQ 64x64 (FID=2.89) [PITH_FULL_IMAGE:figures/full_fig_p022_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Samples generated with PFGM++ (D=128,NFE=79) teacher on FFHQ 64x64 (FID=2.43) [PITH_FULL_IMAGE:figures/full_fig_p022_40.png] view at source ↗
Figure 41
Figure 41. Figure 41: Samples generated with our IPFM (D=inf,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p022_41.png] view at source ↗
Figure 42
Figure 42. Figure 42: Samples generated with our IPFM (D=inf,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p022_42.png] view at source ↗
Figure 43
Figure 43. Figure 43: Samples generated with our IPFM (D=inf,NFE=1, [PITH_FULL_IMAGE:figures/full_fig_p022_43.png] view at source ↗
Figure 44
Figure 44. Figure 44: Samples generated with our IPFM (D=inf,NFE=2, [PITH_FULL_IMAGE:figures/full_fig_p022_44.png] view at source ↗
Figure 45
Figure 45. Figure 45: Samples generated with PFGM++ (D=inf,NFE=5) teacher on FFHQ 64x64 (FID [PITH_FULL_IMAGE:figures/full_fig_p023_45.png] view at source ↗
Figure 46
Figure 46. Figure 46: Samples generated with PFGM++ (D=inf,NFE=13) teacher on FFHQ 64x64 [PITH_FULL_IMAGE:figures/full_fig_p023_46.png] view at source ↗
Figure 47
Figure 47. Figure 47: Samples generated with PFGM++ (D=inf,NFE=31) teacher on FFHQ 64x64 (FID=2.84) [PITH_FULL_IMAGE:figures/full_fig_p023_47.png] view at source ↗
Figure 48
Figure 48. Figure 48: Samples generated with PFGM++ (D=inf,NFE=79) teacher on FFHQ 64x64 (FID=2.53) [PITH_FULL_IMAGE:figures/full_fig_p023_48.png] view at source ↗

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    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

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    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command n...

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    \@lbibitem[] @bibitem@first@sw\@secondoftwo \@lbibitem[#1]#2 \@extra@b@citeb \@ifundefined br@#2\@extra@b@citeb \@namedef br@#2 \@nameuse br@#2\@extra@b@citeb \@ifundefined b@#2\@extra@b@citeb @num @parse #2 @tmp #1 NAT@b@open@#2 NAT@b@shut@#2 \@ifnum @merge>\@ne @bibitem@first@sw \@firstoftwo \@ifundefined NAT@b*@#2 \@firstoftwo @num @NAT@ctr \@secondoft...

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    @open @close @open @close and [1] URL: #1 \@ifundefined chapter * \@mkboth \@ifxundefined @sectionbib * \@mkboth * \@mkboth\@gobbletwo \@ifclassloaded amsart * \@ifclassloaded amsbook * \@ifxundefined @heading @heading NAT@ctr thebibliography [1] @ \@biblabel @NAT@ctr \@bibsetup #1 @NAT@ctr @ @openbib .11em \@plus.33em \@minus.07em 4000 4000 `\.\@m @bibit...