ContinualFlow: Learning and Unlearning with Neural Flow Matching

Davide Bacciu; Lorenzo Simone; Shuangge Ma

REVIEW 4 major objections 5 minor 15 references

ContinualFlow: Learning and Unlearning with Neural Flow Matching

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read A reweighted flow-matching loss makes generative unlearning possible without the forget samples, using only an energy proxy.

desk verdict A correct but essentially tautological importance-reweighting identity, with an unresolved q0 ambiguity that undermines the central sample-free unlearning claim; clearly written and honest, but not a substantive contribution as it stands. read the letter →

arxiv 2506.18747 v1 pith:KKYGGBHQ submitted 2025-06-23 cs.LG cs.AI

Lorenzo Simone , Davide Bacciu , Shuangge Ma This is my paper · ORCID

classification cs.LGcs.AI

keywords machineunlearningflowmatchingenergy-basedmodelsgenerativeimportanceweightingdistributionaltransportcontinuallearningsoftmasssubtraction

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 tries to establish that generative unlearning can be done by reweighting a flow-matching objective instead of retraining, fine-tuning, or accessing the forget samples. It proposes ContinualFlow, which multiplies each training sample's velocity-matching loss by a sigmoid weight $\sigma(-\lambda F(x_1))$ built from an energy function $F(x)$ that scores how strongly a point belongs to the undesired content. The paper proves that this reweighted loss has the same gradient, up to a positive constant, as conditional flow matching toward the soft mass-subtracted target $\tilde{q}_1(x) \propto q_0(x)\,\sigma(-\lambda F(x))$. If correct, a model trained on full data can be steered away from high-energy regions using only an energy proxy and samples from the base distribution, preserving retained-content fidelity. Experiments on 2D benchmarks, MNIST digit removal, and CIFAR-10 latent class suppression show behavior comparable to retraining.

What carries the argument

The central object is the Energy-Reweighted Flow Matching loss, a conditional flow matching objective in which every displacement sample $(x_0, x_1)$ is weighted by $\sigma(-\lambda F(x_1))$, with $\sigma$ the logistic sigmoid and $\lambda$ a suppression scale. The energy function $F(x) \propto -\log q_f(x)$ acts as a scalar potential that is high where the forget distribution is dense, and the sigmoid weight softly down-weights those regions. The argument runs through the identity $\tilde{q}_1(x)/q_0(x) \propto \sigma(-\lambda F(x))$, which makes the weighted loss exactly a constant multiple of the CFM loss toward the soft mass-subtracted target $\tilde{q}_1$. This identity converts unlearning into an importance-sampling reweighting of the standard flow-matching objective, and Algorithm 1 instantiates it by sampling both endpoints from $q_0$ and normalizing the weighted loss by the sum of weights.

What would settle it

On a 2D synthetic example, compute the intended target $\tilde{q}_1(x) \propto q_0(x)\,\sigma(-\lambda F(x))$ by high-resolution numerical integration, train ContinualFlow, and compare generated samples to that density with maximum mean discrepancy. If the trained flow does not approach its own stated target, the optimization claim fails; if it matches the target but the target excludes the wrong regions, the energy proxy is the component to blame.

Watch

Extended reading notes

Core claim

The central claim is Theorem 4.1: for a base distribution $q_0$, a forget energy $F(x) \propto -\log q_f(x)$, and $\lambda > 0$, the Energy-Reweighted Flow Matching loss with weights $\sigma(-\lambda F(x_1))$ satisfies $\nabla_\theta L_{\mathrm{ERFM}}(\theta) = C\,\nabla_\theta L_{\mathrm{CFM}}^{q_0 \to \tilde{q}_1}(\theta)$ with $C > 0$, where $\tilde{q}_1 \propto q_0(x)\,\sigma(-\lambda F(x))$. Because the weight equals the density ratio $\tilde{q}_1(x_1)/q_0(x_1)$, the result follows from importance sampling: reweighting samples drawn from $q_0$ by the sigmoid replaces the endpoint distribution $q_0$ by the reweighted target $\tilde{q}_1$. The paper presents this identity as the reason unlearning can be performed without forget samples: the energy acts as a soft mask that lowers the contribution of high-energy trajectories. The same mechanism extends to classifiers, where the Bayes-optimal classifier logit defines $F$, and to reversing the energy to recover previously forgotten content.

Load-bearing premise

The method depends on trusting that the energy function accurately marks the content to be forgotten and that the base distribution used for sampling is the right starting point; if either is wrong, the flow is steered toward the wrong target.

Editorial extensions

If this is right

A pretrained flow can be re-targeted to a soft mass-subtracted distribution using only an energy proxy and samples from the base distribution, so forget sets need not be stored or replayed.
The suppression strength is controlled by the scalar $\lambda$, giving a continuous knob from no forgetting to near-complete erasure of the high-energy region.
Reversing the sign of the energy reorients the learned flow toward the previously suppressed content, so forgotten classes can be restored without sample access.
Because the objective is a reweighted version of standard flow matching, the same training loop and architecture apply to any flow-based generative model.
Composing multiple energy functions is allowed by the construction, making incremental and continual unlearning a sequence of energy updates rather than retraining.

Reading between the lines

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

Because the weight $\sigma(-\lambda F(x_1))$ is exactly the density ratio defining $\tilde{q}_1$, the equivalence in Theorem 4.1 holds by construction; the substantive question shifts to whether $\tilde{q}_1$, so defined, is the retained distribution the practitioner actually wants.
When the energy is derived from a classifier trained to separate $q_f$ from $q_0$, the effective target depends on $q_0$; if $q_0$ is a fixed Gaussian prior rather than the original model's output distribution, the flow is reweighted toward a reweighted prior, not necessarily the data manifold.
The latent-space image experiments suggest a practical recipe that the paper leaves implicit: train an autoencoder, perform unlearning in the latent space where a semantic classifier is easier to define, then decode, and the same energy-reweighting theorem applies unchanged.
A direct stress test of the framework would be a sequence of concept removals with a time-varying energy, checking whether the flow stays on the retained manifold and whether reversing an earlier energy restores the original behavior.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The headline: this is a cleanly written paper with a correct but essentially tautological theorem, and a clear gap between the theory and the claimed unlearning capability. If you're looking for a case study in how importance-weighting can masquerade as a new method, this is a useful one — but as a contribution to generative unlearning, the central claim doesn't hold up.

What's genuinely new: framing unlearning as reweighting the flow-matching training pairs with a sigmoid energy weight, and showing that this is equivalent to CFM toward a reweighted target. The proof is correct, but it's direct importance sampling: w(x1) is exactly the density ratio tilde q1/q0, so the equivalence holds by construction. The paper does some things well: it's clearly written, notation is consistent, the visualizations of reversible energy guidance on MNIST are nice, and the discussion of composability is a reasonable conceptual point.

The problems. First, the load-bearing ambiguity: Algorithm 1 samples both x0 and x1 from q0, but the paper never fixes what q0 is. Table 2 lists "model output or prior." If q0 is the base prior, then ERFM learns a transport from prior to reweighted prior — not to retained data — so the 2D and image successes shouldn't happen under that reading. If q0 is the pretrained model's output distribution, you need the original model at generation time, meaning no deployed unlearning occurs. Theorem 4.1 only proves equivalence to CFM toward reweighted q0; nothing connects that target to Dretain. That's the gap. Second, the experiments are weak: only retrain and fine-tuning baselines, no existing unlearning methods; the 2D fine-tuning rows are identical to retrain to four decimals, which suggests fine-tuning isn't actually changing the model; CIFAR-10 results are worse than retrain on forget rate and leakage. Third, the evaluation may reuse the same classifier that defines the energy function, which would make the suppression metrics circular.

None of this is a takedown. The paper is honest about the difficulty of learning good energy functions, and the theoretical claim is stated accurately. But the central promise — sample-free unlearning without retaining the original model — is not met. I'd recommend desk rejection; if the authors fix the q0 specification and add proper baselines, there might be a workshop-level contribution here.

Referee Report

4 major / 5 minor

Summary. The paper introduces ContinualFlow, a framework for targeted unlearning in generative flow models. The method, Energy-Reweighted Flow Matching (ERFM), samples endpoint pairs (x0, x1) from a source distribution q0 and minimizes a Conditional Flow Matching (CFM) loss weighted by sigma(-lambda F(x1)), where F is a scalar energy function intended to score association with a forget distribution. The authors define a reweighted target q̃1(x) proportional to q0(x) sigma(-lambda F(x)) and prove (Theorem 4.1) that the ERFM gradient equals, up to a positive constant, the CFM gradient toward q̃1. They also derive a classifier-based energy approximation (Proposition B.1), describe a sample-based OT-CFM variant, and report experiments on four 2D benchmarks, MNIST digit removal, and CIFAR-10 class suppression, with metrics including MMD, retention accuracy, forget rate, leakage, and training time.

Significance. If the central claims held, ContinualFlow would offer a principled, sample-free way to remove undesired content from a pretrained generative model without retraining. The paper is clearly written and the formal statements are internally consistent. Credit is due for spelling out the reweighted-target formulation and for attempting to connect loss-level weights to a distributional target. However, Theorem 4.1 is essentially an importance-sampling identity: the target is defined as proportional to q0 times the weight, so the equivalence between the weighted loss and CFM toward the reweighted target holds by construction and does not by itself establish any unlearning property. The unresolved ambiguity about q0, the absence of any prior-art unlearning baseline, the implausible identical fine-tuning rows in Table 3, and the worse-than-retrain forgetting metrics on CIFAR-10 jointly undermine the empirical and conceptual claims. The result, as it stands, does not support the paper's stated contributions.

major comments (4)

[Section 4.2, Theorem 4.1] Theorem 4.1 is correct but tautological. Since q̃1(x1)/q0(x1) is proportional to sigma(-lambda F(x1)) by the definition of q̃1 in Section 4.1, the ERFM objective is exactly the CFM objective with importance-sampling weights, and the claimed equality of gradients is the standard identity for importance-weighted CFM. The theorem therefore does not establish that optimizing the loss removes the forget distribution; it only shows that the loss matches a reweighted target that was chosen in advance. The central theoretical support for the method is an identity, not a substantive statement about unlearning.
[Section 4.1, Algorithm 1, Table 2] The paper never fixes the source distribution q0, and the two possible readings both break the central 'sample-free unlearning of a pretrained generative model' claim. Algorithm 1 samples both x0 and x1 from q0. If q0 is a fixed base prior, then the learned flow transports the prior to a reweighted version of that same prior; because a generic Gaussian prior contains no data-specific modes, generation from the resulting model cannot reproduce D_retain, and there is no mechanism by which class- or region-specific modes are learned. If instead q0 is the output distribution of the pretrained model G_theta (as suggested by Section 3.1 and Appendix C), then the original model is required to sample q0 at every training step and at every generation step after unlearning, so the original model is never actually removed from the deployment pipeline. The paper must specify which reading is used in each experiment and explain how sampling is performed after unlearning; without this, the central claim is not well-defined.
[Section 5, Table 3 and Table 1] The empirical comparison is not sufficient to support the paper's claims. In Table 3, the fine-tuning rows are identical to the retrain rows to at least four decimals for Circles, Checkerboard, Moons, and 6 Gaussians across every metric except training time, which suggests that the fine-tuning baseline is not actually trained or the numbers were copied from the retrain column; as reported, this baseline provides no information. In the 6-Gaussians row, the proposed method is worse than the identical retrain/fine-tuning baseline on every forgetting metric (MMD 0.0370 vs 0.0303, forget rate 0.0302 vs 0.0018, leakage 0.0338 vs 0.0031). In Table 1, the CIFAR-10 forget rate and leakage for Ours (0.1704 and 0.1748) are worse than retrain (0.1127 and 0.1546), directly contradicting the claim of unlearning performance comparable to retraining. No prior-art unlearning method is used as a baseline anywhere.
[Appendix D, evaluation metrics] The evaluation protocol may be circular, and this is load-bearing for the reported forget-rate improvements. Retention accuracy, forget rate, and leakage are computed with a pretrained binary classifier (Appendix D), while the energy function F in Section 4.1 is described as a proxy scoring association with the forget distribution. If the same classifier supplies both the training weight sigma(-lambda F(x1)) and the evaluation score, then the forget-rate and leakage numbers are partly a self-fulfilling consequence of optimizing against the evaluator. The paper never states whether the classifier used for evaluation is distinct from the classifier used to define F, nor how the energy function is obtained for MNIST and CIFAR-10 beyond the general description of a proxy.

minor comments (5)

[Section D.3] The sampling description in D.3 ('base Gaussian via conditional flow, followed by energy-reweighted transformation') is ambiguous between a fixed latent Gaussian and the output distribution of the pretrained flow; this ambiguity should be resolved for reproducibility.
[Section 3.1] Case 1 (sample-based unlearning with full access) is described in Section 3.1 and revisited in Appendix C, but no experiments or results are reported for it; either add results or explicitly state that Case 1 is only a conceptual setup.
[Various figures] Figure 5 contains garbled axis labels consisting of repeated '/uni...' strings; the figure should be regenerated before any resubmission.
[Abstract and Section 3.2] The abstract states the method works 'without requiring direct access to the samples to be unlearned,' but Proposition B.1 requires a Bayes-optimal classifier trained to distinguish qf from q0, which in practice requires forget-set samples or labels; the practical requirements for obtaining F should be stated explicitly.
[Table 3] The reported inference times (e.g., 0.004 ms) appear implausibly small for image-domain generation and the units are inconsistently formatted; please verify the measurements and clearly state the integration-step settings.

Circularity Check

1 steps flagged · score 7.0 of 10

Theorem 4.1 is an importance-sampling identity: the target q̃1 is defined to contain exactly the loss weight σ(−λF), so the claimed gradient equivalence holds by construction.

self definitional [Section 4.1 (definition of q̃1) and Appendix B.1 (proof of Theorem 4.1)]
"The corresponding normalized target distribution is: q̃1(x) = 1/Z R̃(x), with Z = ∫ q0(x)σ(−λF(x))dx. ... By definition of q̃1, we can express the sampling as a reweighted importance sampling from q0: q̃1(x1)/q0(x1)∝σ(−λF(x1)). Hence, the CFM loss from q0 to q̃1 can be written as ... = C−1·L_ERFM(θ) for some C > 0, which implies: ∇θL_ERFM(θ) = C·∇θL_CFM^{q0→q̃1}(θ)."

Section 4.1 defines the soft mass-subtracted target as q̃1(x) ∝ q0(x)·σ(−λF(x)), and Eq. (3) plus Algorithm 1 use exactly σ(−λF(x1)) as the ERFM weight. Therefore the density ratio q̃1/q0 is σ(−λF)/Z by construction, and the B.1 'proof' merely rewrites CFM toward q̃1 as an importance-weighted expectation over q0. The stated theorem—gradient equivalence between ERFM and CFM toward the reweighted target—is thus an identity, not a derived result. The paper presents this identity as the theoretical justification for unlearning, but it only restates the chosen suppression weight as the target distribution; it does not independently establish that this reweighting corresponds to removing forget-region mass from a trained generative model.

full rationale

The central theoretical claim reduces by construction: the target distribution q̃1 is defined in Section 4.1 as q0(x)σ(−λF(x)), and the ERFM loss weights each CFM term by the same σ(−λF(x1)). Appendix B.1 then proves Theorem 4.1 by observing that q̃1(x1)/q0(x1) ∝ σ(−λF(x1)), which is exactly the importance-weight identity. The theorem is correct, but it is a definitional equivalence rather than an independent derivation of unlearning; it formalizes the chosen reweighting without justifying that this reweighting removes the intended information from the model. The empirical results on 2D benchmarks, MNIST, and CIFAR-10 are external and not themselves circular, so the paper is not wholly tautological. I did not count the unresolved q0 ambiguity (Table 2 lists q0 as 'model output or prior', while Algorithm 1 samples both endpoints from q0) as a demonstrated circular step: under the prior reading the target is a reweighted prior rather than retained data, and under the model-output reading the original model remains needed for sampling, but this is a correctness and privacy gap rather than a derivation that reduces to its own inputs. The evaluation's forget-rate and leakage metrics use a classifier that may be the same object as the energy proxy, but the paper does not explicitly state this identity, so I refrain from treating it as demonstrated circularity. No load-bearing self-citation chain or imported uniqueness theorem was found; the flow-matching foundations cited are external and verifiable.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central theorem is an importance-sampling identity; the only free scalar is lambda, and the main assumptions are the availability and correctness of the energy proxy and the choice of q0.

free parameters (1)

lambda (suppression sensitivity) = 5 in Figure 5; swept 0.5, 2, 5, 1000 in Figure 3
Chosen by hand without a stated selection rule; results depend on it.

assumptions (4)

domain assumption An energy function F(x) proportional to -log q_f(x) is available and accurately reflects the forget distribution.
Sections 3.2 and 4.1; the method never observes forget samples, so the entire unlearning signal comes from F. Proposition B.1 requires a Bayes-optimal classifier.
ad hoc to paper The reweighted distribution q0(x) sigma(-lambda F(x)) is a faithful surrogate for the retained data distribution D_retain.
Section 4.1 constructs the target as q0 reweighted; no argument links this to the actual retained distribution, especially when q0 is a Gaussian prior or model output.
domain assumption q0 is known, samplable, and can serve as both source and proposal distribution for importance sampling.
Algorithm 1 samples x0 and x1 both from q0; if q0 is the original model's output, generating samples requires access to the pretrained model, which the paper does not state at inference.
standard math CFM and OT-CFM convergence and optimal transport coupling results from Tong et al. (2023) and Benamou (2021) hold.
Appendix C invokes these to justify the transport formulation.

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Cite this review

Pith. "Pith review of ContinualFlow: Learning and Unlearning with Neural Flow Matching." pith.science (2026). https://pith.science/paper/KKYGGBHQ

@misc{pith2026250618747,
  author       = {Pith},
  title        = {Pith review of: ContinualFlow: Learning and Unlearning with Neural Flow Matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KKYGGBHQ}},
  note         = {Machine review of arXiv:2506.18747}
}

read the original abstract

We introduce ContinualFlow, a principled framework for targeted unlearning in generative models via Flow Matching. Our method leverages an energy-based reweighting loss to softly subtract undesired regions of the data distribution without retraining from scratch or requiring direct access to the samples to be unlearned. Instead, it relies on energy-based proxies to guide the unlearning process. We prove that this induces gradients equivalent to Flow Matching toward a soft mass-subtracted target, and validate the framework through experiments on 2D and image domains, supported by interpretable visualizations and quantitative evaluations.

Figures

Figures reproduced from arXiv: 2506.18747 by the authors.

**Figure 1.** Conceptual overview of ContinualFlow. Left: Standard learning via Flow Matching, where a neural vector field vθ(t, x) maps a base distribution to a known target. Right: Energyguided unlearning, where the flow is softly modulated by a proxy σ(−λF(x)) to steer trajectories away from undesirable regions without access to samples or exact densities. Recent research on generative machine unlearning primarily focuses on… view at source ↗

**Figure 2.** Top: 2D Circles. A model trained on both rings Dfull is guided by F(x) (blue surface) to suppress the outer ring Dforget and generate inner-ring. Bottom: MNIST. Starting from a model trained on all digits. The top row uses F(x) to guide trajectories toward even digits (Dretain), suppressing odds; the bottom row inverts the energy, redirecting flow to generate odd digits. In [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Effect of suppression factor λ. Top row: The energy function F(z) is low on Dretain (digit “0”) and high on Dforget (digits “1–9”). As λ increases (λ ∈ {0.5, 2, 5, 1000}), the model progressively suppresses Dforget, converging toward samples from Dretain. Bottom row: Reversing F(z) to penalize digit “0” instead, the model excludes Dretain as λ grows. This demonstrates energy-guided modulation of generation in Contin… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: CIFAR-10 latent unlearning. Generation from the full distribution (left), and after suppressing all classes except automobile (middle) and airplane (right), which are assigned low energy. CIFAR-10: Finally, we evaluate ContinualFlow on CIFAR-10 by operating in a 64-dim…

**Figure 5.** Figure 5: The left panel shows the target density as a surface plot, with the corresponding energy function F(x) rendered on the floor plane. The right panel illustrates the learned and unlearned trajectories for four 2D benchmarks: Circles, Moons, 6 Gaussians, and Checkerboard.…

**Figure 6.** Figure 6: Hardware specifications used for 2D and image-domain experiments. D.3. Architectural Details for Latent-Space Image Generation For image-based experiments on MNIST and CIFAR-10, we employ a modular autoencoder–flow pipeline composed of a convolutional encoder, a transp…

**Figure 7.** Figure 7: Comparative architecture diagram of the encoder–decoder models designed for MNIST and CIFAR-10 experiments. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

Review history (2 revisions) →

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Works this paper leans on

15 extracted references · 11 canonical work pages

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safe completion

Interpolated conditional LCFM Flow Matching loss Z Normalization constant LERFM Energy-Reweighted FM loss A. Additional Related Work on Generative Machine Unlearning To contextualize recent advances in generative model unlearning, we organize key works by their approach and focus area, emphasizing methods that directly tackle unlearning or targeted remova...

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6 ICML 2025 Workshop on Machine Unlearning for Generative AI B. Flow Matching Toward Soft Mass-Subtracted Distributions. B.1. Proof of Theorem 4.1 Letq0(x) be a known base density, and letF (x)∝− logqf(x) be an energy function for an unknown forget distribution qf(x). We define the soft mass-subtracted target as ˜R(x)∝q0(x)·σ(−λF (x)), and let ˜q1(x) = ˜R...

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Generation from the full distribution (left), and after suppressing all classes except automobile (middle) and airplane (right), which are assigned low energy

CIFAR-10 latent unlearning. Generation from the full distribution (left), and after suppressing all classes except automobile (middle) and airplane (right), which are assigned low energy. CIFAR-10: Finally, we evaluate ContinualFlow on CIFAR-10 by operating in a 64-dimensional latent space derived from a pretrained autoencoder. This experiment tests the m...

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denotes the set of all couplings with marginalsq0 andq1. The dynamic formulation of optimal transport (Benamou-Brenier (Benamou, 2021)) seeks a time-varying densitypt and vector fieldut that minimize: inf pt,ut Z 1 0 Z Rd pt(x)∥ut(x)∥2dxdt, (5) subject to the continuity equation ∂pt ∂t +∇· (ptut) = 0, with boundary conditionsp0 =q0,p1 =q1. Flow Matching w...

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The right panel illustrates the learned and unlearned trajectories for four 2D benchmarks: Circles, Moons, 6 Gaussians, and Checkerboard

The left panel shows the target density as a surface plot, with the corresponding energy functionF (x) rendered on the floor plane. The right panel illustrates the learned and unlearned trajectories for four 2D benchmarks: Circles, Moons, 6 Gaussians, and Checkerboard. The parameterλ = 5 is used for each experiment. 11 ICML 2025 Workshop on Machine Unlear...

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

safe completion

Interpolated conditional LCFM Flow Matching loss Z Normalization constant LERFM Energy-Reweighted FM loss A. Additional Related Work on Generative Machine Unlearning To contextualize recent advances in generative model unlearning, we organize key works by their approach and focus area, emphasizing methods that directly tackle unlearning or targeted remova...

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Flow Matching Toward Soft Mass-Subtracted Distributions

6 ICML 2025 Workshop on Machine Unlearning for Generative AI B. Flow Matching Toward Soft Mass-Subtracted Distributions. B.1. Proof of Theorem 4.1 Letq0(x) be a known base density, and letF (x)∝− logqf(x) be an energy function for an unknown forget distribution qf(x). We define the soft mass-subtracted target as ˜R(x)∝q0(x)·σ(−λF (x)), and let ˜q1(x) = ˜R...

work page 2025

[3] [4]

Generation from the full distribution (left), and after suppressing all classes except automobile (middle) and airplane (right), which are assigned low energy

CIFAR-10 latent unlearning. Generation from the full distribution (left), and after suppressing all classes except automobile (middle) and airplane (right), which are assigned low energy. CIFAR-10: Finally, we evaluate ContinualFlow on CIFAR-10 by operating in a 64-dimensional latent space derived from a pretrained autoencoder. This experiment tests the m...

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doi: 10.18653/v1/2023

Association for Computational Linguistics. doi: 10.18653/v1/2023. emnlp-main.174. Xu, H., Zhao, N., Yang, L., Zhao, S., Deng, S., Wang, M., Hooi, B., Oo, N., Chen, H., and Zhang, N. Relearn: Unlearning via learning for large language models. arXiv preprint arXiv:2502.11190,

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0”, andDforget includes digits “1–9

and the forget setDforget includes odd digits (1, 3, 5, 7, 9). 9 ICML 2025 Workshop on Machine Unlearning for Generative AI In Figure 3, we visualize generation behavior in a different, more constrained setting. Here,Dretain consists solely of digit “0”, andDforget includes digits “1–9”. As shown in the top row, increasing the energy scaling parameter λ p...

work page 2025

[6] [10]

denotes the set of all couplings with marginalsq0 andq1. The dynamic formulation of optimal transport (Benamou-Brenier (Benamou, 2021)) seeks a time-varying densitypt and vector fieldut that minimize: inf pt,ut Z 1 0 Z Rd pt(x)∥ut(x)∥2dxdt, (5) subject to the continuity equation ∂pt ∂t +∇· (ptut) = 0, with boundary conditionsp0 =q0,p1 =q1. Flow Matching w...

work page 2021

[7] [11]

(8) OT-CFM Justification

=x1−x0. (8) OT-CFM Justification. Proposition 3.4 of Tong et al. (2023) proves that when the couplingπ(x0,x

work page 2023

[8] [15]

The right panel illustrates the learned and unlearned trajectories for four 2D benchmarks: Circles, Moons, 6 Gaussians, and Checkerboard

The left panel shows the target density as a surface plot, with the corresponding energy functionF (x) rendered on the floor plane. The right panel illustrates the learned and unlearned trajectories for four 2D benchmarks: Circles, Moons, 6 Gaussians, and Checkerboard. The parameterλ = 5 is used for each experiment. 11 ICML 2025 Workshop on Machine Unlear...

work page 2025