LDLMIn construction

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Meshchaninov et al. · May 2026Diffusion language model

Sampler

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

TrainingGeneration
Latents at time tz[B, T, 768]Previous estimateẑsc[B, T, 768]Adaptive time grid1,024 stepst[B]
DenoiserOpen →
z0[B, T, 768]
ϵ^\hat\epsilon==(zt−αtz^0)/σt({\htmlData{light=state}{z_t}}-\alpha_t{\htmlData{light=prediction denoiser}{\hat z_0}})/\sigma_tss==−ϵ^/σt-\hat\epsilon/\sigma_tff==−12βtzt−βts-\tfrac12\beta_t{\htmlData{light=state}{z_t}}-\beta_tsmt′{\htmlData{light=step-mean mean}{m_{t'}}}==zt+f (t′−t){\htmlData{light=state}{z_t}}+f\,(t'-{\htmlData{light=time grid}{t}})zt′{\htmlData{light=next-state diffuse}{z_{t'}}}==mt′+βt (t−t′)  ξ{\htmlData{light=step-mean mean}{m_{t'}}}+\sqrt{\beta_t\,({\htmlData{light=time grid}{t}}-t')}\;\xi
mt′[B, T, 768]zt′[B, T, 768]starts as Gaussian noisereplaced by the next latentsstarts as zerosreplaced by this call’s predictionthe next call’s latentsreturned by the last callcall 1 of 1,024 · m: the step’s mean, before its noise · t′: the grid’s next time · α, σ, β: the schedule at t · ξ: fresh Gaussian noise
in
ztz_t [B batch, T positions, 768 d]
out
mt′m_{t'} [B batch, T positions, 768 d]zt′z_{t'} [B batch, T positions, 768 d]z^0\hat z_0 [B batch, T positions, 768 d]
parameters
132,836,352
mode
generation · call 1 of 1,024
state
kept between calls: the latents and the previous estimate, two tensors [B, T, 768], both replaced at every call
Parameters

132,836,352 parameters per call, across its learned components

Exact per-instance accounting
ComponentCalculationParameters
Denoiser132,836,352 across its components132,836,352
Per-instance total132,836,352

Across 1024 shared calls: 132,836,352×1=132,836,352132{,}836{,}352 \times 1 = 132{,}836{,}352 parameters.

Derived from the pinned implementation’s constructors and configuration. The checkpoint’s tensors have not been counted. 306,011,162 of these parameters are trained; frozen GPT-2 and the decoder’s mask vector, 124,442,112, are not.

Sources7

Direct evidence

Sampling starts from the prior with a zero self-conditioning estimate, uses the averaged denoiser, takes the adaptive grid when it is requested and the sampler has been updated and a uniform grid otherwise, steps N times carrying the state and the clean estimate, and returns the last step’s mean.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

One Euler–Maruyama step: the mean is x + drift · dt, and the next state adds diffusion · √(−dt) · noise; the clean estimate is returned with them.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

The reverse SDE: drift −β x/2 − β · score and diffusion √β; the ODE halves the score term and has no diffusion.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

The denoiser’s clean prediction is converted into the noise estimate and the score with the marginal’s mean and standard deviation.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

The generation grid: N + 1 times at equal steps of the weights’ cumulative distribution, interpolated inside bins, clamped to the stopping time, in decreasing order.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

Diffusion: self-conditioning on, `t_min` 0.05 and `eps` 10⁻⁵; the adaptive time sampler has 100 bins, a minimum weight of 0.0001, an EMA of 0.9 and updates every 5,000 steps; the denoiser’s EMA decay is 0.9999; scheduler `tanh` with d = 3, solver `euler`, `ode_sampling` false, N = 128 by default; the denoiser has 12 blocks of width 768 with 12 heads, time conditioning `adaln`, a standard MLP, softcap 50 and self-conditioning by concatenation; the timestep embedding’s `max_period` is 10.

The implementation, pinned at revision e18c42acdfb7, not yet public

Direct evidence

The documented OpenWebText invocation: the joint task on 1,024-token sequences, decoder noise 3, hidden state −3, 1,024 diffusion steps on the adaptive grid.

The implementation, pinned at revision e18c42acdfb7, not yet public