LDLMIn construction

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Meshchaninov et al. · May 2026Diffusion language model

Pinned implementation and paper LDLM @ e18c42a, not yet public · arXiv:2605.07933v1 · OpenWebText · 1024 · checkpoint, tokenizer and saved statistics not verified · How to read

Training Generation

GPT-2 Smallhidden state −3124M weightsstandardized Open →

Latent encoder Open →

z₀ Decoder noise

+\,3\,\epsilon

Latent decoder Open →

Token decoder Open →

L Token cross-entropy

\mathcal L_{w}=\operatorname{CE}(L,\,I)

Feature reconstruction

\mathcal L_{h}=\operatorname{MSE}(\hat h,\,h)

z_t=\alpha_t z_0+\sigma_t\epsilon

z_t t z₀

Denoiser Open →

z₀ Diffusion loss

\mathcal L_{\mathrm{diff}}=\operatorname{MSE}(\hat z_0,\,z_0)

learns from

\mathcal L_{h}\cdot\mathcal L_{\mathrm{diff}}

learns from

\mathcal L_{\mathrm{diff}}

learns from

\mathcal L_{h}

learns from

\mathcal L_{w}

joint objective: the three losses are added, and one backward pass trains the four networksfrozenGPT-2 Small →∇ × γ ∇ × 0

Token loss

tensor

One number for the batch.

shape: $\mathcal L_{w}$ [1 one value]

Sources

Contextual evidence from Token cross-entropy

Reconstruction: Gaussian noise of fixed standard deviation is added to the latents, the latent decoder runs, the token decoder reads its output detached, and the cross-entropy against the token IDs is taken; the latent decoder’s output is also compared with the standardized features by a mean squared error.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Token cross-entropy

Cross-entropy and mean squared error are averaged over valid positions.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Token cross-entropy

Joint training: decoder noise of standard deviation 3; weights 1 for the three losses; the diffusion gradient into the encoder rises from 0.001 over 50,000 steps by a straight-through scaling; the token decoder’s input is detached; AdamW at 3·10⁻⁴ for 1,000,000 steps of 512 sequences, gradients clipped at norm 1.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Joint objective

Diffusion: a time is sampled, the latents are noised by the marginal, with probability one half a first call without gradient gives the self-conditioning estimate, the denoiser predicts the clean latents, and the mean squared error against them is taken; the three losses are summed with their weights.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Joint objective

The optimizer takes every parameter of the four networks that requires a gradient.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Joint objective

The optimizer is AdamW with the configured learning rate, weight decay, betas and epsilon; the schedule is a cosine scheduler given the minimum learning rate, the warm-up’s first rate and its length.

The implementation, pinned at revision e18c42acdfb7, not yet public

Contextual evidence from Joint objective

A step: the gradient is clipped, the optimizer steps, and the moving average of the denoiser is updated.

The implementation, pinned at revision e18c42acdfb7, not yet public