o io@sddlZddlmZmZddlZdejdejdededejf dd Zdd ejd ejd ejdejdede dejfddZ dd ejd ejd ejdejdede de dejfddZ ddedededeeejefgeffddZ dS)N)UnionCallablest solver_ordertau_treturnc Csd|d}||}tj||j|jd}||||| |}|d|d}|d} | d| d} |dkrJ| |t|} t |ddkdd} | |  } | |S)uCompute (1 + tau^2) * integral of exp((1 + tau^2) * x) * x^p dx from s to t with exp((1 + tau^2) * t) factored out, using integration by parts. Integral of exp((1 + tau^2) * x) * x^p dx = product_terms[p] - (p / (1 + tau^2)) * integral of exp((1 + tau^2) * x) * x^(p-1) dx, with base case p=0 where integral equals product_terms[0]. where product_terms[p] = x^p * exp((1 + tau^2) * x) / (1 + tau^2). Construct a recursive coefficient matrix following the above recursive relation to compute all integral terms up to p = (solver_order - 1). Return coefficients used by the SA-Solver in data prediction mode. Args: s: Start time s. t: End time t. solver_order: Current order of the solver. tau_t: Stochastic strength parameter in the SDE. Returns: Exponential coefficients used in data prediction, with exp((1 + tau^2) * t) factored out, ordered from p=0 to p=solver_order−1, shape (solver_order,). )dtypedevicer?g) torcharanger r exp unsqueezelgammamathlogwheretril) rrrrtau_mulhpproduct_terms_factoredrecursive_depth_mat log_factorialrecursive_coeff_matsignsr9/mnt/c/Users/fbmor/ComfyUI/comfy/k_diffusion/sa_solver.pycompute_exponential_coeffs s  r!F sigma_next curr_lambdaslambda_slambda_tis_corrector_stepc Csd|d}||}||}|r(|d||} || || } n|d||d|d|} || || } t| | gS)z`Compute simple order-2 b coefficients from SA-Solver paper (Appendix D. Implementation Details).r r g?)rexpm1negrstack) r"r#r$r%rr&rralpha_tb_1b_2rrr (compute_simple_stochastic_adams_b_coeffs5s   r.simple_order_2c Csj|jd}|r|dkrt||||||St||||}tj||ddj} tj| |} ||} | | S)aCompute b_i coefficients for the SA-Solver (see eqs. 15 and 18). The solver order corresponds to the number of input lambdas (half-logSNR points). Args: sigma_next: Sigma at end time t. curr_lambdas: Lambda time points used to construct the Lagrange basis, shape (N,). lambda_s: Lambda at start time s. lambda_t: Lambda at end time t. tau_t: Stochastic strength parameter in the SDE. simple_order_2: Whether to enable the simple order-2 scheme. is_corrector_step: Flag for corrector step in simple order-2 mode. Returns: b_i coefficients for the SA-Solver, shape (N,), where N is the solver order. rr T) increasing) shaper.r!rvanderTlinalgsolver) r"r#r$r%rr/r& num_timestepsexp_integral_coeffsvandermonde_matrix_Tlagrange_integralsr+rrr !compute_stochastic_adams_b_coeffsEs   r:r start_sigma end_sigmaetacs(dttjtfdtffdd }|S)aReturn a function that controls the stochasticity of SA-Solver. When eta = 0, SA-Solver runs as ODE. The official approach uses time t to determine the SDE interval, while here we use sigma instead. See: https://github.com/scxue/SA-Solver/blob/main/README.md sigmarcs<dkrdSt|tjr|}|krkrSdS)Nrg) isinstancerTensoritem)r>r<r=r;rr tau_funcqs  z'get_tau_interval_func..tau_func)rrr@float)r;r<r=rCrrBr get_tau_interval_funcgs$ rE)F)FF)r ) rtypingrrrr@intrDr!boolr.r:rErrrr s$2+64"