Initial release

engine/plugins/solvers/unipc.lua

@@ -0,0 +1,158 @@
+-- unipc.lua: UniPC (Unified Predictor-Corrector, 2 NFE)
+-- B(h)1 variant with data prediction in log-SNR space.
+
+solver = {
+    name        = "unipc",
+    display     = "UniPC (2 NFE)",
+    description = "Unified predictor-corrector in log-SNR space",
+    nfe         = 2,
+    order       = 2,
+    needs_model = true,
+    stateful    = true,
+    stochastic  = false,
+}
+
+local history = {}  -- {model_output={}, t=float}
+local max_order = 2
+
+local function lambda(t)
+    t = math.max(t, 1e-7); t = math.min(t, 1 - 1e-7)
+    return math.log((1 - t) / t)
+end
+
+local function expm1(x) return math.exp(x) - 1 end
+
+local function solve_1x1(R, b) return {b[1] / (math.abs(R[1]) > 1e-12 and R[1] or 1)} end
+
+local function solve_2x2(R, b)
+    local det = R[1]*R[4] - R[2]*R[3]
+    if math.abs(det) < 1e-12 then return {0, 0} end
+    local inv = 1 / det
+    return {(R[4]*b[1] - R[2]*b[2]) * inv, (R[1]*b[2] - R[3]*b[1]) * inv}
+end
+
+local function solve(K, R, b)
+    if K == 1 then return solve_1x1(R, b)
+    elseif K == 2 then return solve_2x2(R, b)
+    else return {0} end
+end
+
+local function bh1_update(xt, vt, t_curr, t_next, n, model_fn, vt_buf, use_corrector)
+    -- Data prediction: D_n = x - t * v
+    local D_n = {}
+    for i = 0, n-1 do D_n[i] = xt[i] - t_curr * vt[i] end
+
+    local lam_curr = lambda(t_curr)
+    local lam_next = lambda(t_next)
+    local h = lam_next - lam_curr
+    local alpha_next = 1 - t_next
+    local sigma_next = t_next
+    local sigma_curr = math.max(t_curr, 1e-7)
+    local hh = -h
+    local B_h = hh
+    local h_phi_1 = expm1(hh)
+
+    local avail = #history
+    local order = math.min(max_order, avail + 1)
+    local K = order
+    local n_D1 = order - 1
+
+    -- h_phi_k sequence
+    local h_phi_k_vals = {h_phi_1}
+    local fact = 1; local hpk = h_phi_1
+    for k = 1, order do
+        hpk = hpk / hh - 1 / fact
+        h_phi_k_vals[k+1] = hpk
+        fact = fact * (k + 1)
+    end
+
+    -- rks, R matrix, b vector
+    local rks = {}
+    for i = 1, n_D1 do
+        local hist_idx = avail - i + 1
+        local lam_hist = lambda(history[hist_idx].t)
+        rks[i] = (lam_hist - lam_curr) / h
+    end
+    rks[n_D1 + 1] = 1
+
+    local R_mat = {}
+    for row = 1, K do
+        for col = 1, K do
+            R_mat[(row-1)*K + col] = rks[col] ^ (row - 1)
+        end
+    end
+
+    local b_vec = {}
+    fact = 1; hpk = h_phi_1
+    for i = 1, K do
+        hpk = hpk / hh - 1 / fact
+        b_vec[i] = hpk * fact / B_h
+        fact = fact * (i + 1)
+    end
+
+    -- D1 differences
+    local d1 = {}
+    for i = 1, n_D1 do
+        local hist_idx = avail - i + 1
+        local D_hist = history[hist_idx].model_output
+        local rk_inv = (math.abs(rks[i]) > 1e-12) and (1 / rks[i]) or 0
+        d1[i] = {}
+        for j = 0, n-1 do d1[i][j] = (D_hist[j] - D_n[j]) * rk_inv end
+    end
+
+    -- Base term
+    local sigma_ratio = (math.abs(sigma_curr) > 1e-7) and (sigma_next / sigma_curr) or 0
+    local x_t_ = {}
+    for i = 0, n-1 do
+        x_t_[i] = sigma_ratio * xt[i] - alpha_next * h_phi_1 * D_n[i]
+    end
+
+    -- Predictor
+    if n_D1 > 0 then
+        local rhos_p
+        if order == 2 then rhos_p = {0.5}
+        else
+            local Kp = K - 1; local R_p = {}
+            for row = 1, Kp do for col = 1, Kp do R_p[(row-1)*Kp+col] = R_mat[(row-1)*K+col] end end
+            rhos_p = solve(Kp, R_p, b_vec)
+        end
+        for i = 0, n-1 do
+            local pred = 0
+            for k = 1, n_D1 do pred = pred + rhos_p[k] * d1[k][i] end
+            xt[i] = x_t_[i] - alpha_next * B_h * pred
+        end
+    else
+        for i = 0, n-1 do xt[i] = x_t_[i] end
+    end
+
+    -- Corrector
+    if use_corrector and model_fn then
+        model_fn(xt, t_next)
+        local D_corr_diff = {}
+        for i = 0, n-1 do
+            local D_corr = xt[i] - t_next * vt_buf[i]
+            D_corr_diff[i] = D_corr - D_n[i]
+        end
+        local rhos_c
+        if order == 1 then rhos_c = {0.5}
+        else rhos_c = solve(K, R_mat, b_vec) end
+
+        for i = 0, n-1 do
+            local corr = 0
+            for k = 1, n_D1 do corr = corr + rhos_c[k] * d1[k][i] end
+            corr = corr + rhos_c[K] * D_corr_diff[i]
+            xt[i] = x_t_[i] - alpha_next * B_h * corr
+        end
+    end
+
+    -- Update history
+    table.insert(history, {model_output = D_n, t = t_curr})
+    while #history > max_order do table.remove(history, 1) end
+end
+
+function step(xt, vt, t_curr, t_prev, n, model_fn, vt_buf)
+    -- Reset state on first step of a new generation
+    if (step_index or 0) == 0 then history = {} end
+
+    bh1_update(xt, vt, t_curr, t_prev, n, model_fn, vt_buf, true)
+end